the klein gordon equation of generalized hulthen potential in complex quantum mechanics we have investigated the reality of exact bound states of complex and or pt symmetric non hermitian exponential type generalized hulthen potential the klein gordon equation has been solved by using the nikiforov uvarov method which is based on solving the second order linear differential equations by reduction to a generalized equation of hypergeometric type in many cases of interest negative and positive energy states have been discussed for different types of complex potentials

gradual spontaneous breakdown of mathcal pt symmetry in a solvable potential a new solvable potential is introduced by transforming the schrodinger equation into the differential equation of the jacobi polynomials the z x variable transformation function depends on two parameters c and and can be obtained implicitly as x z the remaining two parameters set the strength of the even and odd potential components systematic analysis is given for c 0 0 when the potential contains the scarf ii and rosen morse i potentials as special cases the normalized bound state solutions are obtained in closed form both in the real and symmetric cases the energy eigenvalues are determined from the roots of a quartic algebraic equation despite this implicitly defined spectrum the spectral structure of the potential can be determined easily in the symmetric case the spontaneous breakdown of symmetry can also be studied in a controllable way and it is found that with increasing non hermiticity the complexification of the energy eigenvalues is a gradual process that starts with the ground state the general form of the potential contains the scarf i rosen morse ii generalized poschl teller eckart symmetric ginocchio and dutt khare varshni dkv potentials too and can be identified as a subclass of the general six parameter natanzon class this article is part of a special issue of journal of physics a mathematical and theoretical devoted to quantum physics with non hermitian operators

on the pseudo hermitian nondiagonalizable hamiltonians we consider a class of possibly nondiagonalizable pseudo hermitian operators with discrete spectrum and we establish for such a class the equivalence between the pseudo hermiticity property and the existence of an antilinear involutory symmetry moreover we prove that this class actually coincides with the one of possibly nondiagonalizable weak pseudo hermitian operators and that in no case unless they are diagonalizable and have a real spectrum they are hermitian with respect to a definite inner product finally we show that a typical degeneracy of the real eigenvalues which reduces to the well known kramers degeneracy in the hermitian case occurs whenever a fermionic possibly nondiagonalizable pseudo hermitian hamiltonian admits an antilinear symmetry like the time reversal operator t some consequences and applications are briefly discussed

non self adjoint hamiltonians defined by riesz bases we discuss some features of non self adjoint hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a riesz basis of hilbert space among other things we give conditions under which these hamiltonians can be factorized in terms of generalized lowering and raising operators

pseudo hermitian continuous time quantum walks in this paper we present a model exhibiting a new type of continuous time quantum walk as a quantum mechanical transport process on networks which is described by a non hermitian hamiltonian possessing a real spectrum we call it pseudo hermitian continuous time quantum walk we introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system we observe that the probability distribution on certain vertices increases compared to that of the hermitian case this formalism makes the transport process faster and can be useful for search algorithms

the diffusion reaction d r hamiltonian and the solutions of certain types of linear and nonlinear d r equations in one dimension with a view to having further insight into the mathematical content of the non hermitian hamiltonian associated with the diffusion reaction d r equation in one dimension we investigate a the solitary wave solutions of certain types of its nonlinear versions and b the problem of real eigenvalue spectrum associated with its linear version or with this class of non hermitian hamiltonians for case a we use the standard techniques to handle the quadratic and cubic nonlinearities in the d r equation whereas for case b a newly proposed method based on an extended complex phase space is employed for a particular class of solutions an ermakov system of equations is also found for the linear case further corresponding to the classical version of the above one dimensional complex hamiltonian an equivalent integrable system of two two dimensional real hamiltonians is suggested

infinite families of non hermitian hamiltonians associated with exceptional xm jacobi polynomials using an appropriate change of variable the schr dinger equation is transformed into a second order differential equation satisfied by recently discovered jacobi type xm exceptional orthogonal polynomials this facilitates the derivation of infinite families of exactly solvable hermitian as well as non hermitian trigonometric scarf potentials and a finite number of hermitian and an infinite number of non hermitian symmetric hyperbolic scarf potentials the bound state solutions of all these potentials are associated with the aforesaid exceptional orthogonal polynomials these infinite families of potentials are shown to be extensions of the conventional trigonometric and hyperbolic scarf potentials by the addition of some rational terms characterized by the presence of classical jacobi polynomials all the members of a particular family of these rationally extended polynomial dependent potentials have the same energy spectrum and possess translational shape invariant symmetry the obtained non hermitian trigonometric scarf potentials are shown to be quasi hermitian in nature ensuring the reality of the associated energy spectra

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

a new pt symmetric complex hamiltonian with a real spectrum we construct an isospectrum system in terms of a real and a complex potential to show that the underlying pt symmetric complex hamiltonian possesses a real spectrum which is shared by its real partner

j self adjoint operators with mathcal c symmetries an extension theory approach a well known tool in conventional von neumann quantum mechanics is the self adjoint extension technique for symmetric operators it is used e g for the construction of dirac hermitian hamiltonians with point interaction potentials here we reshape this technique to allow for the construction of pseudo hermitian j self adjoint hamiltonians with complex point interactions we demonstrate that the resulting hamiltonians are bijectively related to the so called hypermaximal neutral subspaces of the defect krein space of the symmetric operator this symmetric operator is allowed to have arbitrary but equal deficiency indices n n general properties of the operators for these hamiltonians are derived a detailed study of operator parametrizations and krein type resolvent formulae is provided for j self adjoint extensions of symmetric operators with deficiency indices 2 2 the technique is exemplified on 1d pseudo hermitian schr dinger and dirac hamiltonians with complex point interaction potentials

resource scalable joint source channel map and mmse estimation of multiple descriptions a joint source channel multiple description jsc md framework for signal estimation and communication in resource constrained lossy networks is presented to keep the encoder complexity at a minimum a signal is coded by a multiple description quantizer mdq with neither entropy nor channel coding the code diversity of mdq and the path diversity of the network are exploited by decoders to combat transmission errors a key design objective is resource scalability powerful nodes in the network can perform jsc md estimation under the criteria of maximum a posteriori probability map or minimum mean square error mmse while primitive nodes resort to simpler md decoding all working with the same mdq code the application of jsc md to distributed estimation of hidden markov models in a sensor network is demonstrated the proposed jsc md map estimator is an algorithm of the longest path in a weighted directed acyclic graph while the jsc md mmse decoder is an extension of the well known forward backward algorithm to multiple descriptions both algorithms simultaneously exploit the source memory the redundancy of the fixed rate mdq and the inter description correlations they outperform the existing hard decision mdq decoders by large margins up to 8 db for gaussian markov sources the complexity of jsc md distributed map sequence estimation can be made as low as that of typical single description viterbi type algorithms

nonlinear pseudo supersymmetry in the framework of fold supersymmetry we recall the importance of recognizing the different mathematical nature of various concepts relating to symmetric quantum theories after clarifying the relation between supersymmetry and pseudo supersymmetry we prove generically that nonlinear pseudo supersymmetry recently proposed by sinha and roy is just a special case of fold supersymmetry in particular we show that all the models constructed by these authors have type a two fold supersymmetry furthermore we prove that an arbitrary one body quantum hamiltonian which admits two local solutions in closed form belongs to type a two fold supersymmetry irrespective of whether or not it is hermitian symmetric pseudo hermitian and so on

large order perturbation theory for a non hermitian pt symmetric hamiltonian a precise calculation of the ground state energy of the complex pt symmetric hamiltonian h p2 14x2 i x3 is performed using high order rayleigh schrodinger perturbation theory the energy spectrum of this hamiltonian has recently been shown to be real using numerical methods here we present convincing numerical evidence that the rayleigh schrodinger perturbation series is borel summable and show that pade summation provides excellent agreement with the real energy spectrum pade analysis provides strong numerical evidence that the once subtracted ground state energy considered as a function of 2 is a stieltjes function the analyticity properties of this stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable hamiltonian h p2 14 x2 ex3

susyqm and other symmetries in quantum mechanics the relation of supersymmetric quantum mechanics susyqm is discussed with two other symmetry based approaches symmetry and a differential realization of the su 1 1 and su 2 algebra it is demonstrated that symmetry imposes conditions on the even and odd parts of the real and imaginary components of the superpotential w x and these are expressed in terms of a system of first order linear differential equations which is homogeneous when the factorization energy is real and inhomogeneous when it is complex the formal solution of this system is presented for various special cases as well as for the general case it is shown that a trivial solution of this system corresponds to the unbroken symmetry for the scarf ii potential the formalism of susyqm is also linked with that of the potential algebra approach and it is demonstrated that the j and j ladder operators of some su 1 1 or su 2 algebras act on series of degenerate levels of different potentials essentially in the same way as the a and a shift operators of susyqm examples are presented for su 1 1 and su 2 potential algebras as well as for spectrum generating algebras of the same type possible generalizations of this construction are also pointed out

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

complexified von roos hamiltonian s η weak pseudo hermiticity isospectrality and exact solvability a complexified von roos hamiltonian is considered and a hermitian first order intertwining differential operator is used to obtain the related position dependent mass weak pseudo hermitian hamiltonians using a liouvillean type change of variables the weak pseudo hermitian von roos hamiltonians hx are mapped into the traditional schr dinger hamiltonian form hq where exact isospectral correspondence between hx and hq is obtained under a user friendly position dependent mass setting it is observed that for each exactly solvable weak pseudo hermitian reference hamiltonian hq there is a set of exactly solvable weak pseudo hermitian isospectral target hamiltonians hx a non hermitian symmetric scarf ii and a non hermitian periodic type symmetric samsonov roy potentials are used as reference models and the corresponding weak pseudo hermitian isospectral target hamiltonians are obtained

complex calogero model with real energies recently the symmetry of many single particle non hermitian hamiltonians has been conjectured to be sufficient to keep their spectrum real we demonstrate this and how the similar concept of a weakened hermiticity can be extended to some exactly solvable two and three particle models

on the pseudo norm and admissible solutions of the symmetric scarf i potential the physically admissible solutions of the symmetric scarf i potential are identified in the domain of real and complex energies it is found that generally there are no admissible complex energy solutions and there is one with real energy in a limited range of the parameters there are two series of seemingly admissible solutions both with the real and complex energies belonging to quasi parity q however the two sets are not orthogonal in the domain of real energies the sign of the pseudo norm of states with real energy is found to oscillate as 1 n in accordance with the example of other symmetric potentials possessing an infinite number of discrete levels it is argued that the spontaneous breakdown of symmetry cannot be defined for the scarf i potential a comparison with some symmetric extensions of the infinite square well is presented

classical trajectories of 1d complex non hermitian hamiltonian systems classical motion of complex 1d non hermitian hamiltonian systems is investigated analytically to identify periodic unbounded and chaotic trajectories expressions for the lyapunov exponent for 1d complex hamiltonians are derived complex potentials and v2 x x3 are studied in detail and their lyapunov exponents are obtained analytically it was found that when is complex all the trajectories of v1 are chaotic with lyapunov exponent im and most of the trajectories of v2 are periodic when is pure imaginary but for other complex values of trajectories of v2 are non periodic and show infinite oscillations unbounded neighbouring trajectories of v2 show power law divergence rather than exponential divergence as in the case of v1

supersymmetric quasi hermitian hamiltonians with point interactions on a loop we explore some aspects of pt symmetric hamiltonians with two point interactions we determine classes of point interactions for which the hamiltonians are supersymmetric we prove that these hamiltonians are quasi hermitian and find a very simple formula for the metric operator and its square root q as well further we present the quasi hermitian hamiltonian with one point interaction with a continuous spectrum

pt symmetric quantum mechanics this paper proposes to broaden the canonical formulation of quantum mechanics ordinarily one imposes the condition h h on the hamiltonian where represents the mathematical operation of complex conjugation and matrix transposition this conventional hermiticity condition is sufficient to ensure that the hamiltonian h has a real spectrum however replacing this mathematical condition by the weaker and more physical requirement h h where represents combined parity reflection and time reversal pt one obtains new classes of complex hamiltonians whose spectra are still real and positive this generalization of hermiticity is investigated using a complex deformation h p2 x2 ix e of the harmonic oscillator hamiltonian where e is a real parameter the system exhibits two phases when e 0 the energy spectrum of h is real and positive as a consequence of pt symmetry however when 1 e 0 the spectrum contains an infinite number of complex eigenvalues and a finite number of real positive eigenvalues b

p mathcal t symmetric non self adjoint operators diagonalizable and non diagonalizable with a real discrete spectrum consider in the operator family h0 a 1a1 a dad d 2 is the quantum harmonic oscillator with rational frequencies w is a symmetric bounded potential and g is a real coupling constant we show that if g being an explicitly determined constant the spectrum of h g is real and discrete moreover we show that the operator has a real discrete spectrum but is not diagonalizable

generalized grassmannian coherent states for pseudo hermitian n level systems the purpose of this paper is to generalize fermionic coherent states for two level systems described by pseudo hermitian hamiltonian cherbal et al 2007 j phys a math theor 40 1835 to n level systems central to this task is the expression of the coherent states in terms of generalized grassmann variables these kinds of grassmann coherent states satisfy the bi overcompleteness condition instead of the overcompleteness one as it is reasonably expected because of the biorthonormality of the system choosing an appropriate grassmann weight function the resolution of identity is examined moreover grassmannian coherent and squeezed states of the deformed group suq 2 for the three level pseudo hermitian system are presented

extended jaynes cummings models and quasi exact solvability the original jaynes cummings model is described by a hamiltonian which is hermitian and exactly solvable here we extend this model by several types of interactions leading to a non hermitian operator which does not satisfy the physical condition of spacetime reflection symmetry pt symmetry the new hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum

pt symmetric models in curved manifolds we consider the laplace beltrami operator in tubular neighborhoods of curves on two dimensional riemannian manifolds subject to non hermitian parity and time preserving boundary conditions we are interested in the interplay between the geometry and spectrum after introducing a suitable hilbert space framework in the general situation which enables us to realize the laplace beltrami operator as an m sectorial operator we focus on solvable models defined on manifolds of constant curvature in some situations notably for non hermitian robin type boundary conditions we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues and establish similarity of the non hermitian m sectorial operators to normal or self adjoint operators the study is illustrated by numerical computations

spiked potentials and quantum toboggans even if the motion of a quantum quasi particle proceeds along a left right symmetric symmetric curved path in complex plane the spectrum of bound states may remain physical i e real and bounded below a generalization is outlined first we show how the topologically less trivial tobogganic contours may be allowed to live on several sheets of a riemann surface second the specification of a scattering regime is formulated for such a class of models

moyal products a new perspective on quasi hermitian quantum mechanics the rationale for introducing non hermitian hamiltonians and other observables is reviewed and open issues identified we present a new approach based on moyal products to compute the metric for quasi hermitian systems this approach is not only an efficient method of computation but also suggests a new perspective on quasi hermitian quantum mechanics which invites further exploration in particular we present some first results which link the berry connection and curvature to non perturbative properties and the metric

pt symmetry cartan decompositions lie triple systems and krein space related clifford algebras gauged quantum mechanics ptqm and corresponding krein space setups are studied for models with constant non abelian gauge potentials and extended parity inversions compact and noncompact lie group components are analyzed via cartan decompositions a lie triple structure is found and an interpretation as symmetrically generalized jaynes cummings model is possible with close relation to recently studied cavity qed setups with transmon states in multilevel artificial atoms for models with abelian gauge potentials a hidden clifford algebra structure is found and used to obtain the fundamental symmetry of krein space related j self adjoint extensions for ptqm setups with ultra localized potentials

delta function potential with a complex coupling we explore the hamiltonian operator where is the dirac delta function and z is an arbitrary complex coupling constant for a purely imaginary z h has a spectral singularity at for re z 0 h has a real positive continuous spectrum that is free from spectral singularities for this latter case we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive definite inner product that renders h self adjoint this allows us to address the intriguing question of the nonlocal aspects of the equivalent hermitian hamiltonian for the system in particular we compute the energy expectation values for various gaussian wave packets to show that the non hermiticity effect diminishes rapidly outside an effective interaction region

mapping of the five parameter exponential type potential model into trigonometric type potentials we choose the five parameter exponential type potential model as input and construct five trigonometric type potentials via point canonical transformations their energy spectra and wavefunctions are obtained in a unified manner by using the expressions for the energy spectra and wavefunctions of the five parameter exponential type potential model

canonical expansion of symmetric operators and perturbation theory let h be any symmetric schrodinger operator of the type 2 x21 x2d igw x1 xd on where w is any odd homogeneous polynomial and it is proved that is self adjoint and that its eigenvalues coincide up to a sign with the singular values of h i e the eigenvalues of moreover we explicitly construct the canonical expansion of h and determine the singular values j of h through the borel summability of their divergent perturbation theory the singular values yield estimates of the location of the eigenvalues j of h by weyl s inequalities

pseudo hermiticity versus pt symmetry ii a complete characterization of non hermitian hamiltonians with a real spectrum we give a necessary and sufficient condition for the reality of the spectrum of a non hermitian hamiltonian admitting a complete set of biorthonormal eigenvectors

non hermitian multi particle systems from complex root spaces we provide a general construction procedure for antilinearly invariant complex root spaces the proposed method is generic and may be applied to any weyl group allowing us to take any element of the group as a starting point for the construction worked out examples for several specific weyl groups are presented focusing especially on those cases for which no solutions were found previously when applied to the defining relations of models based on root systems this usually leads to non hermitian models which are nonetheless physically viable in a self consistent sense as they are antilinearly invariant by construction we discuss new types of calogero models based on these complex roots in addition we propose an alternative construction leading to q deformed roots we employ the latter type of roots to formulate a new version of affine toda field theories based on non simply laced root systems these models exhibit on the classical level a strong weak duality in the coupling constant equivalent to a lie algebraic duality which is known for the quantum version of the undeformed case

a framework for discrete integral transformations i the pseudopolar fourier transform the fourier transform of a continuous function evaluated at frequencies expressed in polar coordinates is an important conceptual tool for understanding physical continuum phenomena an analogous tool suitable for computations on discrete grids could be very useful however no exact analogue exists in the discrete case in this paper we present the notion of pseudopolar grid pp grid and the pseudopolar fourier transform ppft which evaluates the discrete fourier transform at points of the pp grid the pp grid is a type of concentric squares grid in which the radial density of squares is twice as high as usual the pp grid consists of equally spaced samples along rays where different rays are equally spaced in slope rather than angle we develop a fast algorithm for the ppft with the same complexity order as the cartesian fast fourier transform the algorithm is stable invertible requires only one dimensional operations and uses no approximate interpolations we prove that the ppft is invertible and develop two algorithms for its inversion iterative and direct both with complexity o n 2 log n where n times n is the size of the reconstructed image the iterative algorithm applies conjugate gradients to the gram operator of the ppft since the transform is ill conditioned we introduce a preconditioner which significantly accelerates the convergence the direct inversion algorithm utilizes the special frequency domain structure of the transform in two steps first it resamples the pp grid to a cartesian frequency grid and then recovers the image from the cartesian frequency grid

one dimensional point interaction with three complex parameters for a pair of non hermitian hamiltonian h and its hermitian adjoint h there are situations in which their eigenfunctions form a biorthogonal system we illustrate such a situation by means of a one particle system with a one dimensional point interaction in the form of the fermi pseudo potential the interaction consists of three terms with three strength parameters gi i 1 2 and 3 which are all complex this complex point interaction is neither hermitian nor invariant in general the s matrix for the transmission reflection problem constructed with h or with h in the usual manner is not unitary but it conforms to the pseudo unitarity that we define the pseudo unitarity is closely related to the biorthogonality of the eigenfunctions the eigenvalue spectrum of h with the complex interaction is generally complex but there are cases where the spectrum is real in such a case h and h form a pseudo hermitian pair

generalized swanson models and their solutions we analyse a class of non hermitian quadratic hamiltonians which are of the form where are real constants with and and are generalized creation and annihilation operators respectively thus these hamiltonians may be classified as generalized swanson models it is shown that the eigenenergies are real for a certain range of values of the parameters a similarity transformation mapping the non hermitian hamiltonian h to a hermitian one h is also obtained it is shown that h and h share identical energies as explicit examples the solutions of a couple of models based on the trigonometric rosen morse i and the hyperbolic rosen morse ii type potentials are obtained we also study the case where the non hermitian hamiltonian is symmetric

spectral analysis of the complex cubic oscillator using the exact semiclassical analysis we study the spectrum of a one parameter family of complex cubic oscillators the invariance property of the complex hamiltonians and the reality property of the spectrum are discussed analytic continuations of the spectrum in the complex parameter and their connections with the resonance problem for the real cubic oscillator are investigated the global analytic structure of the spectrum yields a branch point structure similar to the multivalued analytic structure discovered by bender and wu for the quartic oscillator

the solution of the schrodinger equation for complex hamiltonian systems in two dimensions we investigate the ground state solutions of the schrodinger equation for complex non hermitian hamiltonian systems in two dimensions within the framework of an extended complex phase space approach the eigenvalues and eigenfunctions of some two dimensional complex potentials are found

exactly solvable non hermitian jaynes cummings type hamiltonian admitting entirely real spectra from supersymmetry it is shown that for a given hermitian hamiltonian possessing supersymmetry there is always a non hermitian jaynes cummings type hamiltonian jcth admitting entirely real spectra the parent supersymmetric hamiltonian and the corresponding non hermitian jcth are simultaneously diagonalizable the exact eigenstates of these non hermitian hamiltonians are constructed algebraically for certain shape invariant potentials including a non hermitian version of the standard jaynes cummings jc model for which the parent supersymmetric hamiltonian is the superoscillator it is also shown that a non hermitian version of the several physically motivated generalizations of the jc model admits entirely real spectra the positive definite metric operator in the hilbert space is constructed explicitly along with the introduction of a new inner product structure so that the eigenstates form a complete set of orthonormal vectors and the time evolution is unitary

calculation of the metric in the hilbert space of a cal p cal t symmetric model via the spectral theorem in a previous paper 1 we introduced a very simple symmetric non hermitian hamiltonian with a real spectrum and derived a closed formula for the metric operator relating the problem to a hermitian one in this paper we propose an alternative formula for the metric operator which we believe is more elegant and whose construction based on a backward use of the spectral theorem for self adjoint operators provides new insights into the nature of the model

some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant comparison between the exact value of the spectral zeta function zh 1 5 6 5 3 2cos 5 2 1 5 3 5 and the results of numeric and wkb calculations supports the conjecture by daniel bessis 1995 private communication that all the eigenvalues of this pt invariant hamiltonian are real for one dimensional schrodinger operators with complex potentials having a monotonic imaginary part the eigenfunctions and the imaginary parts of their logarithmic derivatives have no real zeros

new quasi exactly solvable sextic polynomial potentials a hamiltonian is said to be quasi exactly solvable qes if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in a closed form an entirely new class of qes hamiltonians having sextic polynomial potentials is constructed these new hamiltonians are different from the sextic qes hamiltonians in the literature because their eigenfunctions obey symmetry rather than hermitian boundary conditions these new hamiltonians present a novel problem that is not encountered when the hamiltonian is hermitian it is necessary to distinguish between the parametric region of unbroken symmetry in which all of the eigenvalues are real and the region of broken symmetry in which some of the eigenvalues are complex the precise location of the boundary between these two regions is determined numerically using the extrapolation techniques and analytically using the wkb analysis

pseudospectra in non hermitian quantum mechanics we propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non hermitian operators we relate pseudospectral properties to quasi hermiticity similarity to self adjoint operators and basis properties of eigenfunctions the abstract results are illustrated by unexpected wild properties of operators familiar from pt symmetric quantum mechanics

the quantum effective mass hamilton jacobi problem in this paper the quantum hamilton jacobi theory based on the position dependent mass model is studied two effective mass functions having different singularity structures are used to examine the morse and poschl teller potentials the residue method is used to obtain the solutions of the quantum effective mass hamilton jacobi equation further it is shown that the eigenstates of the generalized non hermitian swanson hamiltonian for morse and poschl teller potentials can be obtained by using the riccati equation without solving a differential equation

calculation of the hidden symmetry operator in symmetric quantum mechanics in a recent paper it was shown that if a hamiltonian h has an unbroken symmetry then it also possesses a hidden symmetry represented by the linear operator the operator commutes with both h and the inner product with respect to is associated with a positive norm and the quantum theory built on the associated hilbert space is unitary in this paper it is shown how to construct the operator for the non hermitian symmetric hamiltonian h 1 2p2 1 2x2 ix3 using perturbative techniques it is also shown how to construct the operator for h 1 2p2 1 2x2 x4 using nonperturbative methods

non hermitian hamiltonian versus e 0 localized states we analyze the zero energy solutions of a two dimensional system which undergoes a non radial symmetric complex potential v r by virtue of the coherent states concept the localized states are constructed and the consequences of the imaginary part of the potential are found both analytically and schematically

metrics and isospectral partners for the most generic cubic pt symmetric non hermitian hamiltonian we investigate properties of the most general symmetric non hermitian hamiltonian of cubic order in the annihilation and creation operators as a ten parameter family for various choices of the parameters we systematically construct an exact expression for a metric operator and an isospectral hermitian counterpart in the same similarity class by exploiting the isomorphism between operator and moyal products we elaborate on the subtleties of this approach for special choices of the ten parameters the hamiltonian reduces to various models previously studied such as to the complex cubic potential the so called swanson hamiltonian or the transformed version of the from below unbounded quartic x4 potential in addition it also reduces to various models not considered in the present context namely the single site lattice reggeon model and a transformed version of the massive sextic x6 potential which plays an important role as a toy model to identify theories with vanishing cosmological constant