decomposition of laguerre polynomials with respect to the cyclic group of order n abstract let n be an arbitrary positive integer we decompose the laguerre polynomials lm as the sum of n polynomials lm n k m n k 0 1 n 1 defined by l m x n k z 1 n t 0 n 1 exp 2i kl n l m x z exp 2i l n z c in this paper we establish the close relation between these components and the brafman polynomials the use of a technique described in an earlier work 2 leads us firstly to derive from the basic identities and relations for lm other analogous for lm n k that turn out to be two integral representations an operational representation some generating functions defined by means of the generalized hyperbolic functions of order n and the hyper bessel functions some finite sums including multiplication and addition formulas a non standard 2n 1 term recurrence relation and a differential equation of order 2n secondly to express some identities of lm as functions of the polynomials lm n k some particular properties of lm n 0 the first component will be pointed out

coherency of su 1 1 barut girardello type and entanglement for spherical harmonics barut girardello coherent states corresponding to the l m and l m integer discrete irreducible representations of su 1 1 lie algebra are calculated by the spherical harmonics ylm their explicit compact forms and also to realize the resolution of the identity their corresponding positive definite measures on the complex plane are obtained in terms of the known functions it is also shown that coherent states of both positive and negative representations separately lead us to construct new representation bases for su 1 1 lie algebra then it is shown that the su 1 1 barut girardello coherent states corresponding to two particles containing the spatial parity symmetries of a bipartite quantum system can be entangled in ten different ways

laguerre type derivatives dobinski relations and combinatorial identities we consider properties of the operators d r m ar a a m which we call generalized laguerre type derivatives with r 1 2 m 0 1 where a and a are boson annihilation and creation operators respectively satisfying a a 1 we obtain explicit formulas for the normally ordered form of arbitrary taylor expandable functions of d r m with the help of an operator relation that generalizes the dobinski formula coherent state expectation values of certain operator functions of d r m turn out to be generating functions of combinatorial numbers in many cases the corresponding combinatorial structures can be explicitly identified

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

multidimensional quasi linear steady infiltration toward a shallow water table the present work explores further a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity on water pressure the green s function method is used to derive a general analytical model pertaining to multidimensional steady infiltration to a shallow water table with arbitrary boundary conditions and arbitrary root uptake forcing functions and for various simple source geometry the general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation and root uptake in the presence of a shallow water table can be easily deduced from the general analytical model new solutions include the one dimensional infiltration subject to discrete extraction functions the two dimensional infiltration from a strip source with a uniform exponential and a periodic flux distribution and the three dimensional infiltration from a rectangular source at the land surface particular solutions have also been obtained for infiltration from a periodic series of point line and strip sources algebraic equations for the parameter estimation of the hydraulic conductivity function were also derived from the simple one dimensional solution the proposed model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest and provides a basis upon which parameter estimation can be effected

barut girardello and klauder perelomov coherent states for the kravchuk functions the barut girardello and klauder perelomov coherent states for the kravchuk functions are constructed it is shown that the resolution of unity condition is satisfied for both of the coherent states also in the n 1 dimensional hilbert space spanned by the kravchuk eigenstates the appropriate measure and analytic function are obtained

shape invariance raising and lowering operators in hypergeometric type equations the schrodinger equations which are exactly solvable in terms of associated special functions are directly related to some self adjoint operators defined in the theory of hypergeometric type equations the fundamental formulae occurring in a supersymmetric approach to these hamiltonians are consequences of some formulae concerning the general theory of associated special functions we use this connection in order to obtain a general theory of schrodinger equations exactly solvable in terms of associated special functions and to extend certain results known in the case of some particular potentials

a class of vector coherent states defined over matrix domains a general scheme is proposed for constructing vector coherent states in analogy with the well known canonical coherent states and their deformed versions when these latter are expressed as infinite series in powers of a complex variable z in the present scheme the variable z is replaced by matrix valued functions over appropriate domains as particular examples we analyze the quaternionic extensions of the canonical coherent states and the gilmore perelomov and barut girardello coherent states arising from representations of su 1 1 possible physical applications are indicated

generalized coherent states for associated hypergeometric type functions we introduce a right inverse for the annihilation operator which appears in the factorization of associated hypergeometric type operators this makes possible the definition of generalized coherent states for the associated eigenfunctions these generalized coherent states satisfy the relevant properties i e label continuity overcompleteness temporal stability and action identity required to establish a close connection between the quantum and classical formulations of a given physical system

burgers equation a general nonlinear solution of infiltration and redistribution 1 the general one dimensional solution of burgers equation is developed using a series of transformations and the green s function method the solution gives the distribution of the reduced water content in a semi infinite and in a finite domain for arbitrary initial moisture distributions the boundary condition at the soil surface can be either a time dependent flux or constant water content while the bottom boundary condition for the finite case is a constant water content value explicit results for a uniform discrete hydrostatic and steady state initial moisture profiles are derived an analytical solution that spans the preponding to the postponding period of rainfall is also obtained expressions for the time to ponding and infiltration equations are presented for the various cases of initial moisture profiles and a shallow water table these results allowed the quantification of the error in the various approximations to the time to ponding and the cumulative infiltration in the postponding period

canonical commutation relations on the interval on the hilbert space h l 2 0 l where 0 l is a bounded interval of r1 the domain for the canonical commutation relation ccr and the ccr quasi algebra is constructed it is shown that the bogolubov inequality for a bose gas in a box is fulfilled

about a new family of coherent states for some su 1 1 central field potentials in this paper we shall define a new family of coherent states which we shall call the mother coherent states bearing in mind the fact that these states are independent from any parameter the bargmann index the rotational quantum number j and so on so these coherent states are defined on the whole hilbert space of the fock basis vectors the defined coherent states are of the barut girardello kind i e they are the eigenstates of the lowering operator for these coherent states we shall calculate the expectation values of different quantum observables the corresponding mandel parameter the husimi s distribution function and also the p function finally we shall particularize the obtained results for the three dimensional harmonic and pseudoharmonic oscillators

factorization little or great algorithm the progress of the factorization method since the 1935 work of dirac is briefly reviewed though linked with older mathematical theories the factorization seems an autonomous driving force offering substantial support to the present day darboux and backlund approaches

an observation of quadratic algebra dual family of nonlinear coherent states and their non classical properties in the generalized isotonic oscillator in this paper we construct nonlinear coherent states for the generalized isotonic oscillator and study their non classical properties in detail by transforming the deformed ladder operators suitably which generate the quadratic algebra we obtain heisenberg algebra from the algebra we define two non unitary and one unitary displacement type operators while the action of one of the non unitary type operators reproduces the original nonlinear coherent states the other one fails to produce a new set of nonlinear coherent states dual pair we show that these dual states are not normalizable for the nonlinear coherent states we evaluate the parameter a3 and examine the non classical nature of the states through quadratic and amplitude squared squeezing effect further we derive analytical formula for the p function q function and the wigner function for the nonlinear coherent states all of them confirm the non classicality of the nonlinear coherent states in addition to the above we obtain the

structure of stieltjes classes of moment equivalent probability laws a stieltjes class is a one parameter family of moment equivalent distribution functions constructed by modulation of a given indeterminate distribution function f called the center of the class members of a stieltjes class are mutually absolutely continuous and conversely any pair of moment equivalent and mutually absolutely continuous distribution functions can be joined by a stieltjes class the center of a stieltjes class is an equally weighted mixture of its extreme members and this places restrictions on which distributions can belong to a stieltjes class with a given center the lognormal law provides interesting illustrations of the general ideas in particular it is possible for two moment equivalent infinitely divisible distributions to be joined by a stieltjes class and random scaling can be used to construct new stieltjes classes from a given stieltjes class

water dynamics in a gradually nonhomogeneous soil described by the linearized richards equation 1 in order to investigate the influence of the soil vertical nonhomogeneity on the dynamics of the water in the upper soil layer an analytical solution of the linearized richards equation was derived here the hydraulic conductivity ks at saturation is assumed to decrease exponentially with depth in accordance with field data reported in the literature and collected during our surveys in mountain catchments gardner s constitutive laws were assumed for the hydraulic conductivity and water retention characteristics k s and s the resulting one dimensional richards equation is linear and its coefficients decrease exponentially with depth an analytical solution was found by using the method of laplace transform and compared with some test cases both analytically and numerically the soil water content profile exhibits a maximum at one point in the domain moreover it accounts for a different behavior in the water dynamics depending on the prevailing role of diffusive effects related to the soil water retention or of the transport effects related to the hydraulic conductivity profile

generation of coherent states of photon added type via pathway of eigenfunctions we obtain and investigate the regular eigenfunctions of simple differential operators xr dr 1 dxr 1 r 1 2 with the eigenvalues equal to 1 with the help of these eigenfunctions we construct a non unitary analogue of a boson displacement operator which will be acting on the vacuum in this way we generate collective quantum states of the fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly these states are thus coherent states in the sense of klauder they span the truncated fock space without first r lowest lying basis states 0 1 r 1 these states are squeezed sub poissonian in nature and reminiscent of photon added states in agarwal and tara 1991 phys rev a 43 492

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

new generalized coherent states we construct a new family of boson coherent states using a specially designed function which is a solution of a functional equation de q x dx e q qx with 0 q 1 and e q 0 1 we use this function in place of the usual exponential to generate new coherent states q z from the vacuum which are normalized and continuous in their label z these states allow the resolution of unity and a corresponding weight function is furnished by the exact solution of the associated stieltjes moment problem they also permit exact evaluation of matrix elements of an arbitrary polynomial given as a normally ordered function of boson operators we exemplify this by showing that the photon number statistics for these states is sub poissonian for any q 1 the states q z are squeezed we obtain and discuss their signal to quantum noise ratio the function e q x allows a natural generation of multiboson coherent states of arbitrary multiplicity which is impossible for the usual coherent states for q 1 all the above resul

general displaced su 1 1 number states revisited the most general displaced number states based on the bosonic and an irreducible representation of the lie algebra symmetry of su 1 1 and associated with the calogero sutherland model are introduced here we utilize the barut girardello displacement operator instead of the klauder perelomov counterpart to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime too with special nonlinearity functions they depend on two parameters and can be converted into the well known barut girardello coherent and number states respectively depending on which of the parameters equal to zero a discussion of the statistical properties of these states is included significant are their squeezing properties and anti bunching effects which can be raised by increasing the energy quantum number depending on the particular choice of the parameters of the above scenario we are able to determine the status of compliance with flexible statistics major parts of the

an exactly solvable periodic schrodinger operator the authors explicitly determine the band spectrum of a periodically strongly singular schrodinger operator in l2 r associated with the differential expression d2 dx2 s2 1 4 cos2 x s 2 1 4 sin2 x x epsilon r x epsilon pi z 2 0 s s 1 the corresponding density of states is calculated analytically

a report on the nonlinear squeezed states and their non classical properties of a generalized isotonic oscillator we construct nonlinear squeezed states of a generalized isotonic oscillator potential we demonstrate the non existence of a dual counterpart of nonlinear squeezed states in this system we investigate the statistical properties exhibited by the squeezed states in particular mandel s parameter second order correlation function photon number distributions and parameter a3 in detail we also examine the quadrature and amplitude squared squeezing effects finally we derive the expression for the s parameterized quasi probability distribution function of these states all this information about the system is new to the literature

representations of coherent states in non orthogonal bases starting with the canonical coherent states we demonstrate that all the so called nonlinear coherent states used in the physical literature as well as large classes of other generalized coherent states can be obtained by changes of bases in the underlying hilbert space this observation leads to an interesting duality between pairs of generalized coherent states bringing into play a gelfand triple of rigged hilbert spaces moreover it is shown that in each dual pair of families of nonlinear coherent states at least one family is related to a generally non unitary projective representation of the weyl heisenberg group which can then be thought of as characterizing the dual pair

on the completeness of photon added coherent states we demonstrate explicitly the completeness of photon added coherent states pacss introduced by agarwal and tara agarwal g s and tara k 1991 phys rev a 43 492 and defined up to normalization by m z m 0 1 2 where is the boson creation operator and z are conventional glauber klauder coherent states we find the analytical form of the positive weight function in their resolution of unity by solving the associated stieltjes power moment problem we furnish an example of generation of another set of pacss which are complete

nonlinear semi coherent states their nonclassical features and phase properties semi coherent states semi css were previously introduced and their nonclassical properties studied in this paper we first propose a general formalism for the construction of nonlinear semi css as an extension of semi css and then their explicit form in the number state basis is generally deduced next as some physical appearances of the formalism after choosing two well known nonlinearity functions nonclassical features and quantum statistical properties of the associated states are studied by evaluating quadrature squeezing higher order squeezing and the mandel parameter as well as their phase properties and number and phase squeezing of the introduced states finally the results are compared with the properties of semi css

nonclassical properties of coherent states and excited coherent states for continuous spectra based on the definition of coherent states for continuous spectra and analogous to photon added coherent states for discrete spectra we introduce the excited coherent states for continuous spectra it is shown that the main axioms of gazeau klauder coherent states will be satisfied properly nonclassical properties and quantum statistics of coherent states as well as the introduced excited coherent states are discussed in particular through the study of quadrature squeezing and amplitude squared squeezing it will be observed that both classes of the above states can be classified in the intelligent states category

multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface the present work explores a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity and the moisture content on water pressure the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration in a semi infinite flow domain with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometry the general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution can be easily deduced from the general analytical model the model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest new explicit solutions have been obtained for one dimensional infiltration under various prescribed time dependent flux boundary conditions and for two and three dimensional moisture redistribution for constant initial or boundary conditions the multidimensional solution is essentially the product of two or three time dependent terms with each term being a function of only one space variable

su 1 1 barut girardello coherent states for landau levels it is shown that the hilbert space corresponding to all the quantum states of the landau problem can be split in two different ways as infinite direct sums of the finite and infinite dimensional representation subspaces of the lie algebras su 2 and su 1 1 with finite and infinite fold degeneracies respectively for each of the hilbert representation subspaces of the lie algebra su 1 1 we construct a suitable linear combination of its bases as the barut girardello coherent states

generalized deformed oscillator corresponding to the modified poschl teller energy spectrum a generalized deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the modified poschl teller potential is constructed for special values of the potential depth the deformed oscillator algebra has a finite dimensional irreducible representation the polynomial representation and the associate deformed operations of integration and differentiation are studied the results of this study are general and they can be applied directly to the case of the q deformed oscillator with q being a root of unity

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

the general structure of eigenvalues in nonlinear oscillators hilbert spaces of bounded one dimensional nonlinear oscillators are studied it is shown that the eigenvalue structure of all such oscillators have the same general form they depend only on the ground state energy of the system and a single function h of the hamiltonian operator h it is also found that the hilbert space of the nonlinear oscillator is unitarily inequivalent to the hilbert space of the simple harmonic oscillator providing an explicit example of haag s theorem a number operator for the nonlinear oscillator is constructed and the general form of the partition function and average energy of a nonlinear oscillator in contact with a heat bath is determined connection with the wkb result in the semiclassical limit is made the analysis is then applied to the case of the x4 anharmonic oscillator as an explicit example

unified approach to the analogues of single photon and multiphoton coherent states for generalized bosonic oscillators a large class of bosonic coherent states known in the literature have been constructed in a unified way by shanta et al 1994 it is shown that this method can be easily extended to generalized bosonic oscillator systems

clean two and three dimensional analytical solutions of richards equation for testing numerical solvers 1 this technical note derives clean analytical solutions of richards equation for three dimensional unsaturated groundwater flow clean means that the boundary conditions and steady state solutions are closed form expressions and the transient solutions have relatively simple additional fourier series terms two dimensional versions of these solutions are also given the primary purpose for the solutions is to test linear and nonlinear solvers in finite difference volume element computer programs for accuracy and scalability using architectures ranging from pcs to parallel high performance computers this derivation starts from the quasi linear assumption of relative hydraulic conductivity varying exponentially with pressure head and the separate approximation that relative hydraulic conductivity varies linearly with moisture content this allows a transformation to be used to create a linear partial differential equation separation of variables and fourier series are then used to obtain the final solution physically reasonable material properties are also used a total of four solutions are given in this technical note steady state and transient solutions for two different boundary conditions of the sample problem

construction of photon added spin coherent states and their statistical properties in the present work we construct and investigate some properties of the photon added spin coherent states pa scss the klauder s minimal set of conditions required to obtain coherent states are discussed we give the analytical form for the positive weight function in the resolution of unity finally we examine the statistical properties of the pa scss in terms of different parameters using the mandel s q parameter all these quantities are expressed in terms of hypergeometric and meijer g functions and so the pa scss are a new field of application for these functions

nonlinear conserved charge coherent state and its relation to nonlinear entangled state by suitably averaging over u 1 group action on a two mode nonlinear coherent state we derive the nonlinear conserved charge coherent state based on it a new nonlinear entangled state f g and its deductive state are introduced their completeness relation is proved a new two mode nonlinear squeezing operator in f g representation is obtained which in turn leads to a nonlinear negative binomial state

on the completeness of coherent states generated by binomial distribution we demonstrate the completeness of boson and spin coherent states generated by binomial distribution by furnishing the exact analytical form of their respective positive weight functions in resolution of unity these weight functions are solutions of the associated truncated stieltjes power moment problem we elaborate on the non unique character of these solutions

deformed photon added nonlinear coherent states and their non classical properties in this paper we will try to present a general formalism for the construction of deformed photon added nonlinear coherent states dpancss f m which in a special case lead to the well known photon added coherent state pacs m some algebraic structures of the introduced dpancss are studied and particularly the resolution of the identity as the most important property of generalized coherent states is investigated meanwhile it will be demonstrated that the introduced states can also be classified in the f deformed coherent states with a special nonlinearity function next we will show that these states can be produced through a simple theoretical scheme a discussion on the dpancss with negative values of m i e f m is then presented our approach has the potentiality to be used for the construction of a variety of new classes of dpancss corresponding to any nonlinear oscillator with known nonlinearity function as well as arbitrary solvable quantum system with known discrete non degenerate spectrum finally after applying the formalism to a particular physical system known as the poschl teller p t potential and the nonlinear coherent states corresponding to a specific nonlinearity function some of the non classical properties such as the mandel parameter second order correlation function in addition to first and second order squeezing of the corresponding states will be investigated numerically

quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation we review the definition of hypergeometric coherent states discussing some representative examples then we study mathematical and statistical properties of hypergeometric schrodinger cat states defined as orthonormalized eigenstates of kth powers of nonlinear f oscillator annihilation operators with f of the hypergeometric type these k hypercats can be written as an equally weighted superposition of hypergeometric coherent states zl l 0 1 k 1 with zl ze2 il k a kth root of zk and they interpolate between number and coherent states this fact motivates a continuous circle representation for high k we also extend our study to truncated hypergeometric functions finite dimensional hilbert spaces and a discrete exact circle representation is provided we also show how to generate k hypercats by amplitude dispersion in a kerr medium and analyze their generalized husimi q function in the super and sub poissonian cases at different fractions of the revival time

barut girardello coherent states of the pseudoharmonic oscillator in the paper we have investigated some properties of the barut giraradello coherent states bgcs the eigenstates of the su 1 1 lowering generator k for the hamiltonian of the pseudoharmonic oscillator pho by using these states the diagonal p representation of the density operator is constructed as a new result for this potential in addition we have calculated some thermal expectation values for the quantum canonical gas of the phos the calculations using the bgcs representation seem to be much simpler and easier to program than the corresponding calculations in other representations e g the position representation at the end of the paper the time dependence of these states is presented

hierarchical dobinski type relations via substitution and the moment problem we consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson a a 1 monomials of the form exp a ra r 1 2 under the composition of their exponential generating functions they turn out to be of sheffer type we demonstrate that two key properties of these sequences remain preserved under substitutional composition a the property of being the solution of the stieltjes moment problem and b the representation of these sequences through infinite series dobinski type relations we present a number of examples of such composition satisfying properties a and b we obtain new dobinski type formulae and solve the associated moment problem for several hierarchically defined combinatorial families of sequences

lie algebras for systems with mixed spectra i the scattering poschl teller potential starting from an n body quantum space we consider the lie algebraic framework where the poschl teller hamiltonian 1 2 2 c sech2 s csch2 is the single sp 2 r casimir operator the spectrum of this system is mixed it contains a finite number of negative energy bound states and a positive energy continuum of free states it is identified with the clebsch gordan series of the d d representation coupling the wave functions are the sp 2 r clebsch gordan coefficients of that coupling in the parabolic basis using only lie algebraic techniques we find the asymptotic behavior of these wave functions for the special pure trough potential s 0 we derive thus the transmission and reflection amplitudes of the scattering matrix

photon added coherent states as nonlinear coherent states the states m defined as up to a normalization constant and where m is a non negative integer are shown to be the eigenstates of where is a nonlinear function of the number operator the explicit form of is constructed the eigenstates of this operator for negative values of m are introduced the properties of these states are discussed and compared with those of the state m the eigenstates corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states m and 0 respectively

mittag leffler coherent states we create a family of boson coherent states using the functions of mittag leffler ml e z 0 and their generalizations e z 0 instead of exponentials these states are shown to satisfy the usual requirements of normalizability continuity in the label and the resolution of unity with a positive weight function this last quantity is found for arbitrary 0 as a solution of an associated stieltjes moment problem in addition for m 1 2 3 and 1 corresponding to em z we propose and analyse special q deformations 0 q1 of the functions em z which serve as a tool to define q deformed coherent states of ml type we provide the expressions for expectation values of physical quantities for all the above states we discuss physical properties of these states noting that they are squeezed the ml coherent states are sub poissonian in nature whereas the q deformed ml states can be sub and super poissonian depending on q all these states are shown to be eigenstates of deformed boson operators whose commutation relations are given

representations of coherent and squeezed states in a f deformed fock space we establish some of the properties of the states interpolating between number and coherent states denoted by n among them are the reproduction of these states by the action of an operator valued function on n the standard fock space and the fact that they can be regarded as f deformed coherent bound states in this paper we use them as the basis of our new fock space which in this case is not orthogonal but normalized then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis finally the statistical properties of these states are studied in detail

coherent states for isospectral oscillator hamiltonians coherent states for a family of isospectral oscillator hamiltonians are derived from a suitable choice of annihilation and creation operators the fock bargmann representation is also considered

coherent states for systems with discrete and continuous spectrum for a system with one degree of freedom coherent states that are parametrized by classical canonical action angle variables are introduced these states also possess continuity of labelling a resolution of unity and temporal stability the insistence on canonical action angle variables strongly restricts any remaining arbitrariness in the coherent state definition such states are introduced for semibounded hamiltonian operators having either a discrete or a continuous spectrum hamiltonians that have both discrete and continuous parts in their spectrum are also discussed

the quasilinear approximation for unsaturated porous media flow this paper gives a review of the quasilinear approximation an exponential relationship between hydraulic conductivity and moisture potential and the uses this has been put to since the time of its creation one of the major attractions of this approximation is that under steady regimes the highly nonlinear richards equation governing unsaturated flow can be linearized this simplification has enabled analytic and semianalytic solutions to be found for many unsaturated flow problems these are reviewed and the current research areas in which the quasilinear approximation is being used are discussed

photon added squeezed vacuum one photon state as an even odd nonlinear coherent state we show that the photon added squeezed vacuum a m s z 0 and the photon added squeezed one photon state a m s z 1 where m is a non negative integer may be regarded as even and odd nonlinear coherent states respectively to achieve this we derive an operator valued function f n m of the number operator n a a such that a m s z i i 0 1 are eigenstates of f n m a 2 based on this and using the unified method developed by shanta et al we find that a m s z i can be equivalently expressed in exponential forms the eigenstates of f n m a 2 are also constructed and their nonclassical features are studied in detail

infiltration models for soil profiles bounded by a water table 1 approximate solutions of richards equation are developed for rational forms of the soil hydraulic conductivity and moisture retention functions using a perturbation expansion method a novel approach is devised in the perturbation technique whereby a priori introduced parameters are estimated in an optimal context to ensure the accuracy of the perturbation solution at all times and for all flow conditions the perturbation model describes the one dimensional nonlinear nonsteady infiltration for arbitrary initial conditions under either a time dependent surface flux or a constant head boundary condition into either a semi infinite or a finite medium bounded from below by a shallow water table the optimal perturbation approach proved to be an effective method by which closed form linear solutions can be adapted to nonlinear soils through proper scaling factors the results show that the first order linear term of the optimal perturbation solution is sufficiently accurate for practical applications especially for shallow water table conditions they offer the means to analyze the effect of nonuniform initial conditions and the influence of the water table on the infiltration process practical results in terms of well defined soil water parameters and the antecedent moisture content include algebraic expressions for the surface moisture content variation under variable rainfall conditions time to ponding expressions and infiltration equations for deep and shallow water table conditions and a prediction formula for the water table recharge rate

on a new gap phenomenon in riemannian geometry abstract this note announces some theorems that show that the flat metric of euclidean space has no nearby nonflat complete metric with the property that its curvature keeps a sign and is uniformly small in a sense made precise here

the construction of some important classes of generalized coherent states the nonlinear coherent states method considering some important classes of generalized coherent states known in the literature we demonstrated that all of them can be created via conventional methods i e the lowering operator eigenstate and the displacement operator techniques using the nonlinear coherent states approach as a result we obtained a unified method to construct a large class of coherent states which have already been introduced by different prescriptions

q ν deformation of generalized basic hypergeometric states we provide with a q deformation of the generalized hypergeometric coherent states defined such that the normalization function is given by generalized basic hypergeometric functions these states are eigenstates of suitably defined deformed lowering operators we study the domain of convergence of the corresponding normalization function on the basis of these states we investigate generalized basic hypergeometric husimi distributions and corresponding phase distributions as well as new analytic basis representations of arbitrary quantum states in bargmann and hardy spaces the quantum statistical properties of the states such as photon counting statistics and quadrature squeezing are analytically and numerically discussed in the framework of conventional quantum optics

generalised coherent states and group representations on hilbert spaces of analytic functions using the example for the group su 1 1 the author obtains the basis functions of a hilbert space of analytic functions from the perelomov 1972 definition of generalised coherent states the lie algebra in this space has the form of a holstein primakoff representation appropriate for su 1 1

new physics in landau levels the most general displaced number coherent states based on the heisenberg su 2 and su 1 1 lie algebras symmetries are constructed they depend on two parameters and can be converted into the well known photon added two variable glauber coherent states and displaced number states respectively depending on which of the parameters is equal to zero the relations of the weyl heisenberg algebra guarantee a corresponding resolution of the identity conditions a discussion of the statistical properties of these states is included significant are their squeezing properties which can be raised by increasing the energy and angular momentum quantum numbers n and m the maximum squeezing is obtained for bext 0 depending on the particular choice of parameters in the above scenarios we are able to determine the status of compliance with poissonian statistics in the limiting case we obtain a major result about the non classical properties of the glauber minimum uncertainty coherent states in other words in addition to the requirement to minimize uncertainty conditions they carry non classical features too finally a theoretical framework is proposed to generate them

spherical harmonics coherent states constructed by the second lowest and second highest bases of su 1 1 lie algebra the second lowest and second highest bases of the discrete positive and negative irreducible representations of su 1 1 lie algebra via spherical harmonics are used to construct generalized coherent states depending on whether the representation label is an even or odd integer each of the new coherent states is separated into two different classes they are constituted by appropriate superpositions of the increasing and decreasing infinite sequences with respect to the m index of the spherical harmonics ym2j m m j 1 and ym2k m 1 m k 2 and converge to the known functions also the non oscillating measures to realize the resolution of the identity condition on the unit disk are calculated

a deformed oscillator with coulomb energy spectrum a deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the coulomb potential is constructed the deformed oscillator algebra has a polynomial realization and the associate deformed operations of integration and differentiation are studied

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

coherent states for nonlinear harmonic oscillator and some of its properties a one dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states we develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on gazeau klauder formalism we analyze their statistical properties by means of mandel parameter and second order correlation function our analysis reveals that the constructed coherent states exhibit super poissonian statistics moreover it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution the validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme

inconsistencies in the description of a quantum system with a finite number of bound states by a compact dynamical group in a recent paper aldaya v and guerrero j 2005 j phys a math gen 38 6939 it is shown that the bound states of the modified poschl teller potential should be described by the non compact dynamical group su 1 1 instead of the usual compact group su 2 here we prove that su 2 cannot be the dynamical group for a potential with a finite number of bound states on the basis of the modified poschl teller potential and the morse potential this suggests that a quantum system with a continuum spectrum and a finite number of bound states should be described both in the continuum and the discrete spectrum by a non compact dynamical group instead of a compact one

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

dynamical symmetry approach to periodic hamiltonians we show that dynamical symmetry methods can be applied to hamiltonians with periodic potentials we construct dynamical symmetry hamiltonians for the scarf potential and its extensions using representations of su 1 1 and so 2 2 energy bands and gaps are readily understood in terms of representation theory we compute the transfer matrices and dispersion relations for these systems and find that the complementary series plays a central role as well as nonunitary representations

multidimensional linearized nonsteady infiltration toward a shallow water table the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration toward a shallow water table with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometries the general green s function solution allows the derivation of particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution the model assumes that the hydraulic conductivity function is an exponential function of the water pressure and a linear function of the moisture content one dimensional solutions are obtained for time dependent distributions of the flux at the land surface and of root uptake in the subsurface two and three dimensional solutions are also derived for point and line sources in the domain for a strip a rectangle and a disc source at the land surface and for two and three dimensional moisture redistribution and root uptake most of the solutions are a product of two terms one term is a function of depth while the other term is a function of time and the lateral coordinates numerical results show the effect of the water table and soil type on the two dimensional moisture movement from a strip source

on tori without conjugate points in this paper we consider riemannian metrics without conjugate points on an n torus recent work of j heber established that the gradient vector fields of busemann functions on the universal cover of such a manifold induce a natural foliation akin to the weak stable foliation for a riemannian manifold with negative sectional curvature on the unit tangent bundle the main result in the paper is that the metric is flat if this foliation is lipschitz we also prove that this foliation is lipschitz if and only if the metric has bounded asymptotes this confirms a conjecture of e hopf in this case

new nonlinear coherent states based on hypergeometric type operators the main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states to do this we first establish a class of hypergeometric type of generalized displacement operators 1fr 0 0 1 r 1 za act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the fock space which admit a resolution of the identity through a positive definite measure on the complex plane furthermore realization of the compact form of these states as functions of the position coordinate x for r 2 leads to a generating function of the hermite polynomials in terms of the modified bessel function finally studying some statistical characters reveals that they have indeed non classical features such as squeezing an anti bunching effect and sub poissonian statistics too

asymptotics of invariant metrics in the normal direction and a new characterisation of the unit disk we give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains specifically we will give the second term in the expansion of the metrics this depends on an improved localisation result and estimates in the one variable case finally we will give a new characterisation of the unit disk in mathbb c in terms of the asymptotic behaviour of quotients of invariant metrics

quantum algebras and q special functions related to coherent states maps of the disc the quantum algebras generated by the coherent states maps of the disc are investigated it is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q analysis the applications of the analysis to star product quantizations and q special functions theory are given among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed when the series is treated as a reproducing kernel

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

generalized heisenberg algebra application to the harmonic oscillator the deformed poisson algebra recently introduced to investigate integrable systems 2003 j phys a math gen 36 12181 203 2005 j math phys 46 042702 is used to perform the transition from the phase space of classical observables functions depending on positions and momentums to the hilbert space of physically well defined hermitian operators a hamiltonian operator for the harmonic oscillator system is constructed and the eigenvalue problem is solved the generalization to an n dimensional space shows that such an algebra does not break the rotational symmetry

photon added barut girardello coherent states of the pseudoharmonic oscillator in a previous paper popov d 2001 j phys a math gen 34 5283 we have constructed the coherent states css of the pseudoharmonic oscillator pho these states are of the barut girardello type in the present paper we have constructed and investigated some properties of the photon added barut girardello coherent states pa bgcss of the pho these states are not orthogonal but are normalized and satisfy a unity resolution relation the completeness relation we have found the analytical form for the positive weight function in the resolution of unity by using these states we have calculated some expectation values the first two powers of the number operator n which have evinced some non classical properties in order to examine the statistical properties of a pho gas which obeys the quantum canonical distribution the diagonal p representation of the density operator m is constructed and the thermal expectation values are calculated all these quantities are expressed in terms of meijer g functions and so the pa bgcss are a new field of application for these functions also the time dependence of the pa bgcss is examined if in the obtained results we put m 0 we recover all the results from our previous paper

one dimensional schrodinger operators with interactions singular on a discrete set on etudie le caractere auto adjoint des operateurs de schrodinger sur y u j i x j y j ou on suppose y j x j 1

asymptotic dirichlet problems for harmonic functions on riemannian manifolds we define the asymptotic dirichlet problem and give a sufficient condition for solving it this proves an existence of nontrivial bounded harmonic functions on certain classes of noncompact complete riemannian manifolds 0 introduction in this paper we will prove the existence of nonconstant bounded harmonic functions on certain classes of noncompact riemannian manifolds by defining and solving an asymptotically defined dirichlet problem for harmonic functions the motivation comes from the classical uniformization theorem of riemann surfaces which says that a simply connected riemann surface is biholo morphic to the riemann sphere s2 the complex plane c or the unit disk d this is a geometric theorem but its original proof due to koebe relies heavily on function theory the function theoretic interpretation of this theorem is the following among the noncompact simply connected surfaces c is characterized by the fact that it admits no nonconstant bounded harmonic functions and d by that it admits nonconstant bounded harmonic functions the geometric aspect of the uniformization theorem could be roughly stated as follows let m be a simply connected riemann surface equipped with a complete riemannian metric with gaussian curvature km if km c 0 then m is biholo morphic to s2 if km c 0 then m is biholomorphic to d if km is close to zero then m is biholomorphic to c the following precise version is due to greene and wu gw1 p 120

generalized grassmann variables for quantum kit k level systems and barut girardello coherent states for su r 1 algebras this paper concerns the construction of su r 1 barut girardello coherent states in terms of generalized grassmann variables we first introduce a generalized weyl heisenberg algebra a r r 1 generated by r pairs of creation and annihilation operators this algebra provides a useful framework to describe qubit and qukit k level systems it includes the usual weyl heisenberg and su 2 algebras we investigate the corresponding fock representation space the generalized grassmann variables are introduced as variables spanning the fock bargmann space associated with the algebra a r the barut girardello coherent states for su r 1 algebras are explicitly derived and their over completion properties are discussed