generalization of the darboux transformation and generalized harmonic oscillators the darbroux transformation is generalized for time dependent hamiltonian systems which include a term linear in momentum and a time dependent mass the formalism for the n fold application of the transformation is also established and these formalisms are applied for a general quadratic system a generalized harmonic oscillator and a quadratic system with an inverse square interaction up to n 2 among the new features found it is shown for the general quadratic system that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution which is related to the existence of coherent states in the system

generalized coherent squeezed and intelligent states for exactly solvable quantum systems and the analogue of the displacement and squeezing operators using an algebraic approach we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder operator and the displacement operator methods showing the equivalence between the two procedures we obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce in a second approach we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators in the first case and the combined action of these operators in the second case we apply the generalized approach for shape invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states

dual state vector of nonlinear coherent state and its application in complex p representation we introduce the dual vector z f n of a single mode nonlinear coherent state ncs by using the contour integral form of function and the explicit form of z f n is obtained in enlarged hilbert space the nonlinear fock states and their contour representation are deduced a new completeness relation composed of z f n and ncs in contour integral form is derived and its application in constructing a complex p representation of density operators is shown

construction of classical superintegrable systems with higher order integrals of motion from ladder operators we construct integrals of motion for multidimensional classical systems from ladder operators of one dimensional systems this method can be used to obtain new systems with higher order integrals we show how these integrals generate a polynomial poisson algebra we consider a one dimensional system with third order ladder operators and found a family of superintegrable systems with higher order integrals of motion we obtain also the polynomial algebra generated by these integrals we calculate numerically the trajectories and show that all bounded trajectories are closed

extensions of exchange rings we define non unital exchange rings and we prove that ifiis an ideal of a ringr thenris an exchange ring if and only ifiandr iare exchange rings and idempotents can be lifted moduloi we also show that we can replace the condition on liftability of idempotents with the condition that the canonical mapk0 r k0 r i be surjective

classes of modules with the exchange property in searching for isomorphic refinements of direct sum decompositions of modules9 crawley and jonsson introduced an exchange property for modules that is strongly reminiscent of steinitz exchange lemma for vector spaces an r module m where r is an associative ring with identity is said to have the finite exchange property if m can be fitted into any finite sum grid as follows whenever a4 occurs as a direct summand of a finite direct sum a bielai then a m ci for suitable submodules ci of the ai 2 this concept led to very general extensions of the classical refinement theorems see e g 2 3 171 many of the problems suggested by crawley and jonsson in their pioneering paper are still open the most salient one does the finite exchange property imply the unrestricted exchange property we show that the answer is yes for modules which possess decompositions into indecomposable summands in the background of this observation stands the following

quasi exactly solvable quartic potential a new two parameter family of quasi exactly solvable quartic polynomial potentials is introduced heretofore it was believed that the lowest degree one dimensional quasi exactly solvable polynomial potential is sextic this belief is based on the assumption that the hamiltonian must be hermitian however it has recently been discovered that there are huge classes of non hermitian symmetric hamiltonians whose spectra are real discrete and bounded below replacing hermiticity by the weaker condition of symmetry allows for new kinds of quasi exactly solvable theories the spectra of this family of quartic potentials discussed here are also real discrete and bounded below and the quasi exact portion of the spectra consists of the lowest j eigenvalues these eigenvalues are the roots of a jth degree polynomial

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

weakly clean rings abstract we study the class of weakly clean rings which were introduced in 15 it is known that weakly clean rings are a subclass of exchange rings and that they contain clean rings as a proper subclass in this paper we prove that weakly clean rings also contain some other important examples of exchange rings such as regular rings and c algebras of real rank zero further we prove that many classes of weakly clean rings can be viewed as corners of clean rings this for example implies that every regular ring and every c algebra of real rank zero is a corner of a clean ring lastly we study the question when the ideal extension of weakly clean rings is weakly clean and we give an example of a non weakly clean exchange ring answering the question in 15

the barut girardello coherent states it is shown that the completeness problem of the sl 2 r coherent states proposed by barut and girardello leads to a moment problem not a mellin transform this moment problem which also appears in the theory of para bose oscillators has been solved following the sharma mehta mukunda sudarshan solution of the problem the matrix element of finite transformation in the coherent state basis is shown to satisfy a quasiorthogonality condition analogous to the orthogonality condition of the matrix element in the canonical basis finally the barut girardello hilbert space of entire analytic functions of growth 1 1 turns out to be only a subspace of bargmann s well known hilbert space of analytic functions this subspace which has been called the reduced bargmann space in a previous paper is an invariant subspace of sl 2 r with this identification the generators of the group in this realization turn out to be the well known boson operators of holman and biedenharn

factorization method and new potentials with the oscillator spectrum a one parameter family of potentials in one dimension is constructed with the energy spectrum coinciding with that of the harmonic oscillator this is a new derivation of a class of potentials previously obtained by abraham and moses with the help of the gelfand levitan formalism

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

bender wu branch points in the cubic oscillator the analytic continuation of the resonances of the cubic anharmonic oscillator to complex values of the coupling constant is studied with semiclassical and numerical methods bender wu branch points at which level crossing occurs are calculated and labelled by a process of analytic continuation the different resonances are the values that a single analytic function takes on different sheets of a riemann surface whose topology is described

diagonalization of matrices over regular rings abstract square matrices are shown to be diagonalizable over all known classes of von neumann regular rings this diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings these results are proved in greater generality namely for matrices and modules over exchange rings where attention is restricted to regular matrices

gromov translation algebras over discrete trees are exchange rings it is shown that the gromov translation ring of a discrete tree over a von neumann regular ring is an exchange ring this provides a new source of exchange rings including for example the algebras g 0 of x matrices over a field of constant bandwidth an extension of these ideas shows that for all real numbers r in the unit interval 0 1 the growth algebras g r introduced by hannah and o meara in 1993 are exchange rings consequently over a countable field countable dimensional exchange algebras can take any prescribed bandwidth dimension r in 0 1

non hermitian matrix description of the calpcalt symmetric anharmonic oscillators the symmetric differential schrodinger equation h e with the operator h h x p2 ax4 i x3 cx2 i x h x on l2 is studied at a 0 it is rearranged as a linear algebraic diagonalization with rigorous proof our non variational construction of bound states offers an infinite dimensional analogue to the recent finite dimensional quasi exact solution available at the less common a 0

supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion the main result of this article is that we show that from supersymmetry we can generate new superintegrable hamiltonians we consider a particular case with a third order integral and apply mielnik s construction in supersymmetric quantum mechanics we obtain a new superintegrable potential separable in cartesian coordinates with a quadratic and quintic integrals and also one with a quadratic integral and an integral of order of 7 we also construct a superintegrable system written in terms of the fourth painleve transcendent with a quadratic integral and an integral of order of 7

coherent states for anharmonic oscillator hamiltonians with equidistant and quasi equidistant spectra two kinds of transformation for the time dependent schrodinger equation i e the differential and integral transformations are introduced if one considers only stationary solutions of this equation both transformations reduce to the well known darboux transformation for the stationary schrodinger equation when applied to non stationary solutions they give different results both transformations are invertible in appropriate spaces with the help of these transformations alternative systems of coherent states to those in the literature are obtained for isospectral hamiltonians with equidistant spectra these transformations are also applied to the construction of coherent states for hamiltonians whose spectrum consists of an equidistant part and one separately disposed level with an energy gap equal to the k skipped levels

on one dimensional schrodinger problems allowing polynomial solutions we discuss the explicit construction of the schrodinger equations admitting a representation through some family of general polynomials almost all solvable quantum potentials are shown to be generated by this approach some generalization has also been performed in higher dimensional problems

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

subnormality and composition operators on h2 if is a non constant analytic function defined on the unit disk d such that d d the composition operator c is the operator on the hardy space h2 of the unit disk defined by c f f in this paper we investigate the relationship between properties of the symbol and the subnormality of the operators c and c the main theorem shows under a regularity hypothesis that c is subnormal if and only if is in a restricted class of linear fractional transformations the two previously known special cases the affine transformations associated with the cesaro operator and the automorphisms are included as the extreme examples the proof of the main theorem consists of verifying a moment condition and yields in addition the construction of a measure that exhibits cgj as multiplication by an analytic function on p2 and the identification of the minimal normal extension as a weighted sum of shifts

on the existence of compressive solitary waves in compacting media necessary conditions for the existence of compressive solitary wave solutions of a partial differential equation derived by scott and stevenson 1986 which describes the two phase fluid flow in a medium compacting under gravity are derived it is shown that for compressive solitary wave solutions to exist which satisfy certain boundary conditions it is necessary that n m 1 where n and m are the exponents in power laws relating the permeability of the medium and the viscosity of the solid matrix respectively to the voidage the effect of the value of the exponents n and m on the shape of the solitary wave is investigated by using existing analytical solutions and new numerical solutions

strong coupling expansions for the symmetric oscillators we study the traditional problem of convergence of perturbation expansions when the hermiticity of the hamiltonian is relaxed to a weaker symmetry an elementary and quite exceptional cubic anharmonic oscillator is chosen as an illustrative example of such models we describe its perturbative features paying particular attention to the strong coupling regime efficient numerical perturbation theory proves suitable for such a purpose

a family of complex potentials with real spectrum we consider a two parameter non hermitian quantum mechanical hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions in contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane our model is integrable along a line parallel to the real axis

distorted heisenberg algebra and coherent states for isospectral oscillator hamiltonians the dynamical algebra associated with a family of isospectral oscillator hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates it is shown that this representation becomes similar to that of the standard heisenberg algebra and it is dependent on a parameter omega or 0 we call it the distorted heisenberg algebra where omega is the distortion parameter the corresponding coherent states for an arbitrary omega are derived and some particular examples are discussed in detail a prescription to produce the squeezing by adequately selecting the initial state of the system is given

exactly solvable hydrogen like potentials and the factorization method a set of factorization energies is introduced giving rise to a generalization of the schrodinger or infeld and hull factorization for the radial hydrogen like hamiltonian an algebraic intertwining technique involving such factorization energies leads us to derive n parametric families of potentials which in general are almost isospectral to the hydrogen like radial hamiltonians the construction of susy partner hamiltonians with ground state energies greater than the corresponding ground state energy of the initial hamiltonian is also explicitly performed

higher order susy linearized nonlinear heisenberg algebras and coherent states using an iterative construction of the first order intertwining technique we find k parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below e0 it is seen that the natural ladder operators for these systems give place to polynomial nonlinear algebras and it is shown that these algebras can be linearized the coherent states construction is performed in the nonlinear and linearized cases

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

square free modules with the exchange property we prove that a square free module with finite exchange has full exchange more generally if r is an exchange ring with r j r abelian and r is endowed with a left linear hausdorff complete topology then r is a full exchange ring this provides an overarching framework for capturing many other results in the literature such as the fact that quasi continuous modules with finite exchange have full exchange we further show that square free modules with exchange satisfy an infinite version of the c3 property

ladder operators for isospectral oscillators we present for the isospectral family of oscillator hamiltonians a systematic procedure for constructing raising and lowering operators satisfying any prescribed distorted heisenberg algebra including the q generalization this is done by means of an operator transformation implemented by a shift operator the latter is obtained by solving an appropriate partial isometry condition in the hilbert space formal representations of the nonlocal operators concerned are given in terms of pseudo differential operators using the new annihilation operators new classes of coherent states are constructed for isospectral oscillator hamiltonians the corresponding fock bargmann representations are also considered with specific reference to the order of the entire function family in each case

factorization method and singular hamiltonians the oscillator singular supersymmetric partners are studied in detail and their relationship with the equivalent problem of an oscillator plus an infinite barrier is clearly established interesting potentials with possible applications to different physical models appear as a bonus

rings of square stable range one abstract a ring s is said to have square stable range one written ssr s 1 if a s b s s implies that a 2 b x is a unit for some x s in the commutative case this extends the class of rings of stable range 1 and allows many new examples such as rings of real valued continuous functions and real holomorphy rings on the other hand ssr s 1 sometimes forces s to have stable range 1 for instance this is the case for exchange rings s for which ssr s 1 is characterized by s rad s being reduced or abelian or right quasi duo we also characterize rings s whose von neumann regular elements are strongly regular by using an element wise notion of square stable range one extending a result of estes and ohm we show that a possibly noncommutative infinite domain with stable range one or square stable range one must have a non artinian group of units

continuous modules are clean ar ingr is said to be clean if every element of r is a sum of an idempotent and a unit the class of clean rings is quite large and includes for instance semiperfect rings and thus finite rings and rings of linear transformations of vector spaces we prove that the endomorphism ring of every continuous or discrete module is clean

stable range one for rings with many idempotents an associative ring r is said to have stable range 1 if for any a b e r satisfying ar br r there exists y e r such that a by is a unit the purpose of this note is to prove the following facts theorem 3 an exchange ring r has stable range 1 if and only if every regular element of r is unit regular theorem 5 if r is a strongly 7r regular ring with the property that all powers of every regular element are regular then r has stable range 1 the latter generalizes a recent result of goodearl and menal 5 let r be an associative ring with identity r is said to have stable range 1 if for any a b e r satisfying ar br r there exists y e r such that a by is a unit this definition is left right symmetric by vaserstein 9 theorem 2 furthermore by a theorem of kaplansky all one sided units are two sided in rings having stable range 1 cf vaserstein 10 theorem 2 6 it is well known that a von neumann regular ring r has stable range 1 if and only if r is unit regular see for example goodearl 4 proposition 4 12 call a ring r strongly 7 regular if for every element a e r there exist a number n depending on a and an element x e r such that an an lx this is in fact a two sided condition 3 it is an open question whether all strongly 7r regular rings have stable range 1 goodearl and menal 5 proved that strongly 7r regular rings are unit regular and hence have stable range 1 theorem 5 8 p 278 in this note we first extend the above result for von neumann regular rings to a larger class of rings which includes all strongly 7r regular rings 7r regular rings von neumann regular rings and algebraic algebras as an application of this we prove that a strongly 7r regular ring r has stable range 1 if powers of every regular element are regular the latter is a generalization of the abovementioned result of goodearl and menal for strongly 7r regular regular rings as one can see from our proofs rings in these classes have a large supply of idempotents throughout r stands for an associative ring with identity and j r for the jacobson radical of r modules are unitary right r modules except otherwise specified for other undefined terms readers are referred to 4 let mr be a right r module following crawley and jonsson 2 mr is said to have the exchange property if for every module ar and any two received by the editors january 24 1994 and in revised form may 3 1994 originally communicated to the proceedings of the ams by k a goodearl 1991 mathematics subject classification primary 1 6d70 1 6p70

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

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

class a composition operators on h2 abstract in this paper we study class a composition operators c on the hardy space h 2 we show that if c belongs to class a then 0 is a fixed point of the symbol as a corollary we obtain that every invertible class a composition operator is unitary moreover we examine spectral properties and the commutants of class a composition operators we also prove that if is a linear fractional self map of d into itself then c belongs to class a if and only if it is subnormal finally we provide some conditions under which c belongs to class a

isospectral hamiltonian for position dependent mass for an arbitrary quantum system and coherent states by means of the unitary transformation a new way for discussing the ordering prescription of the schrodinger equation with a position dependent mass pdm for isospectral hamiltonian operators is presented we show that the ambiguity parameter choices in the kinetic part of the hamiltonian can be explained through an exact susy qm symmetry as well as a consequence of an accidental symmetry under the z2 action by making use of the unitary transformation we construct coherent states for a family of pdm isospectral hamiltonians from a suitable choice of ladder operators we show that these states preserve the usual structure of klauder perelomov s states and thus saturate and minimize the position momentum uncertainty relation pmur under some special restrictions we show that pmur properties can be used to determine the sign of the superpotential

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

the structure of countably generated projective modules over regular rings abstract we prove that for every regular ring r there exists an isomorphism between the monoids of isomorphism classes of finitely generated projective right modules over the rings end r r r and rcfm r where the latter denotes the ring of countably infinite row and column finite matrices over r we use this result to give a precise description of the countably generated projective modules over simple regular rings and over regular rings satisfying s comparability

isospectral susy potentials the authors introduce a new linear transformation in order to construct isospectral potentials within the framework of supersymmetric quantum mechanics under this transformation the adjoint character of the ladder operator is destroyed but with preservation of the energy spectrum leading to some interesting consequences such as the concept of pseudo partnership of the two components connection with the darboux theorem as well as with some other recent methods of construction is analysed

factorization of sturm liouville operators solvable potentials and underlying algebraic structure in this paper a general method of factorization of sturm liouville sl operators is provided a method to solve sl eigenvalue problems is presented new classes of exactly solvable potentials are obtained the supersymmetry and shape invariance approaches are generalized to the sl operators it is shown that the sl shape invariance potentials have an underlying algebraic structure this algebra is in general infinite dimensional the condition of finite algebra is obtained

on rings whose projective modules have the exchange property it is well known that all projective modules over a perfect ring have the exchange property this was shown by yamagata 32 and independently by harada and ishii lo provided that the identity of the ring can be expressed as a sum of orthogonal primitive idempotents the converse is also true 32 that it fails in general was demonstrated by kutami and oshiro ls who constructed a nonartinian boolean ring whose projective modules nevertheless have the exchange property as it turned out this outsider example is representative of an extensive class of rings in fact both perfect and regular rings are subsumed in the hypotheses of the following

characterizations of binormal composition operators with linear fractional symbols on h2 for an analytic function d d the composition operator c is the operator on the hardy space h2 defined by c f f for all f in h2 in this paper we give necessary and sufficient conditions for the composition operator c to be binormal where the symbol is a linear fractional selfmap of d furthermore we show that c is binormal if and only if it is centered when is an automorphism of d or z sz t s t 1 we also characterize several properties of binormal composition operators with linear fractional symbols on h2

invariant vector fields and the prolongation method for supersymmetric quantum systems the kinematical and dynamical symmetries of equations describing the time evolution of quantum systems such as the supersymmetric harmonic oscillator in one space dimension and the interaction of a non relativistic spin one half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method generators of supersymmetries are then introduced so that we get lie superalgebras of symmetries and supersymmetries this approach does not require the introduction of grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry the jaynes cummings model and supersymmetric generalizations are then studied we show how it is closely related to the preceding models lie algebras of symmetries and supersymmetries are also obtained

fock bargmann representation of the distorted heisenberg algebra the dynamical algebra associated with a family of isospectral oscillator hamiltonians named distorted heisenberg algebra because of its dependence on a distortion parameter has recently been studied the connection of this algebra with the hilbert space of entire analytic functions of growth is analysed

generally deformed oscillator isospectral oscillator system and hermitian phase operator the generally deformed oscillator gdo and its multiphoton realization as well as the coherent and squeezed vacuum states are studied we discuss in particular the gdo depending on a complex parameter q therefore we call it q gdo together with the finite dimensional cyclic representations as a realistic physical system of a gdo the isospectral oscillator system is studied and it is found that its coherent and squeezed vacuum states are closely related to those of the oscillator it is pointed out that starting from the q gdo with q root of unity one can define the hermitian phase operators in quantum optics consistently and algebraically the new creation and annihilation operators of the pegg barnett type phase operator theory are defined by using the cyclic representations and these operators degenerate to those of the ordinary oscillator in the classical limit

nonlinear coherent states for nonlinear systems in this work we construct nonlinear coherent states for hamiltonians with linear and quadratic terms in the number operator by the generalization of two definitions as eigenstates of a deformed annihilation operator and as those states obtained by the application of a deformed displacement operator on the vacuum state we evaluate their temporal dependence analyze its dispersion relations and some of their statistical properties for two model hamiltonians one supporting a finite number of bound states and the other supporting an infinite number of bound states

metric completions of ordered groups and k0 of exchange rings we give a description of the closure of the natural affine continuous function representation of k0 r for any exchange ring r this goal is achieved by extending the results of goodearl and handelman about metric completions of dimension groups to a more general class of pre ordered groups which includes k0 of exchange rings as a consequence the results about k 0 of regular rings which the author gave in an earlier paper can be extended to a wider class of rings which includes c algebras of real rank zero among others also the framework of pre ordered groups developed here allows other potential applications

half orthogonal sets of idempotents we improve several results in the literature focused on lifting idempotents by either removing the lifting hypothesis or weakening other assumptions we prove that countable sets of idempotents which are orthogonal modulo an enabling ideal lift to orthogonal idempotents left associates of liftable idempotents also lift modulo the jacobson radical additionally we exhibit situations when half orthogonal sets of idempotents can be orthogonalized by multiplying by a unit we finish by proving a number of results on directs sums of modules with the exchange property

lifting units in clean rings abstract let r be a clean ring with an ideal i such that r i is semiperfect and k 0 i is torsion free we prove that under some mild conditions units in r i can be lifted to units in r this implies that the matrix ring m n r over bergman s example of a non clean exchange ring r is not clean for every n we also obtain some other results concerning lifting units in clean rings

polynomial heisenberg algebras polynomial deformations of the heisenberg algebra are studied in detail some of their natural realizations are given by the higher order susy partners and not only by those of first order as is already known of the harmonic oscillator for even order polynomials here it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd moreover it will be proved that the general systems ruled by such kinds of algebras in the quadratic and cubic cases involve painleve transcendents of types iv and v respectively

accurate eigenvalues and eigenfunctions for quantum mechanical anharmonic oscillators the representation of the taylor expansion of the logarithmic derivative of the wavefunction by means of a pade approximant followed by an appropriate quantization condition proves a powerful way of obtaining accurate eigenvalues of the schrodinger equation in this paper we investigate in detail some of the interesting features of this approach termed riccati pade method rpm by means of its application to anharmonic oscillators we analyse the occurrence of many roots in the neighborhoods of the physical eigenvalues in the weak coupling regime and also obtain accurate coefficients of the strong coupling expansion we finally investigate the global and the local accuracy of the rpm eigenfunctions

on generalized coherent states with maximal symmetry for the harmonic oscillator generalized coherent states for the one dimensional harmonic oscillator with maximal symmetry i e admitting the semidirect sum so 2 1 h 2 as the largest invariance lie algebra pointed out by niederer are constructed the normalization of such states as well as their completeness property are determined and discussed they are also analyzed in the subcontexts of the so 2 1 algebra and of the heisenberg h 2 algebra general considerations on heisenberg relations on minimal dispersions and on quantum mechanical entropies are presented in connection with the uncertainty principle

darboux transformations of coherent states of the time dependent singular oscillator darboux transformation of both barut girardelo and perelomov coherent states for the time dependent singular oscillator is studied in either case a measure that realizes the resolution of the identity operator in terms of coherent states is found and a corresponding holomorphic representation is constructed for the particular case of the free particle moving with the fixed value of the square of angular momentum equal to 2 it is shown that the barut giriardelo coherent states are more localized at the initial time moment while the perelomov coherent states are more stable with respect to time evolution it is also illustrated that darboux transformation may keep unchanged this different time behaviour

phase operators temporally stable phase states mutually unbiased bases and exactly solvable quantum systems we introduce a one parameter generalized oscillator algebra that covers the case of the harmonic oscillator algebra and discuss its finite and infinite dimensional representations according to the sign of the parameter we define an hamiltonian operator associated with and examine the degeneracies of its spectrum for the finite when 0 and the infinite when 0 representations of we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators to overcome the difficulties related to the phase operator in the infinite dimensional case and to avoid the degeneracy problem for the finite dimensional case we introduce a truncation procedure which generalizes the one used by pegg and barnett for the harmonic oscillator this yields a truncated generalized oscillator algebra where s denotes the truncation order we construct two types of temporally stable states for as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of two applications are considered in this paper the first concerns physical realizations of and in the context of one dimensional quantum systems with finite morse system or infinite poschl teller system discrete spectra the second deals with mutually unbiased bases used in quantum information

supersymmetry factorisation of the schrodinger equation and a hamiltonian hierarchy the author presents a systematic procedure for constructing a hierarchy of non relativistic hamiltonians with the property that the adjacent members of the hierarchy are supersymmetric partners i e they share the same eigenvalue spectrum except for the missing ground state and the eigenvectors are simply related