Related papers: PT-symmetric non-polynomial oscillators and hyperb…
A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed…
We prove that the purely imaginary square well generates an infinite number of bound states with real energies. In the strong-coupling limit, our exact PT symmetric solutions coincide, utterly unexpectedly, with their textbook, well known…
We suggest a general ansatz for the energy-eigenstates when a complex one-dimensional PT-symmetric potential possesses real discrete spectrum. Several interesting features of PT-symmetric quantum mechanics have been brought out using this…
The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows all real eigen-energy spectrum.…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary…
Sturmian bound states emerging at a fixed energy and numbered by a complete set of real eigencouplings are considered. For Sturm-Schroedinger equations which are manifestly non-Hermitian we outline the way along which the correct…
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special…
We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-time-symmetric relativistic model possessing two interacting scalar complex fields. The phase diagram contains stable PT-symmetric regions and…
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V equations…
We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly…
Infinite families of quasi-exactly solvable position-dependent mass Schr\"odinger equations with known ground and first excited states are constructed in a deformed supersymmetric background. The starting points consist in one- and…
Balanced gain and loss leads to stationary dynamics in open systems. This occurs naturally in PT-symmetric systems, where the imaginary part of the potential describing gain and loss is perfectly antisymmetric. While this case seems…
The ${\cal PT}$ symmetric version of the generalised Ginocchio potential, a member of the general exactly solvable Natanzon potential class is analysed and its properties are compared with those of ${\cal PT}$ symmetric potentials from the…