Related papers: New rational extensions of solvable potentials wit…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…
Convergence of the Schwinger --- DeWitt expansion for the evolution operator kernel for special class of potentials is studied. It is shown, that this expansion, which is in general case asymptotic, converges for the potentials considered…
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
An alternative approximation scheme has been used in solving the Schrodinger equation to the more general case of exponential screened Coulomb potential, V(r)=-(a/r)\[1+(1+br)e^{-2br}]. The bound state energies of the 1s, $2s, and…
This paper deals with global dispersive properties of Schr\"odinger equations with real-valued potentials exhibiting critical singularities, where our class of potentials is more general than inverse-square type potentials and includes…
In this letter we study a class of symmetries of the new translational extended shape invariant potentials. It is proved that a generalization of a compatibility condition introduced in a previous article is equivalent to the usual shape…
The strictly nonrelativistic isospectral scheme based on the general Riccati solution and Darboux transformation function corresponding to excited states is presented on the following examples: the harmonic oscillator, the square well, and…
We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
In this paper, the approximate analitical solutions of the hyper-radial Schr\"{o}dinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy…
The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb…
Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…
A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and…
Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…
We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials…