Related papers: A new exactly integrable hypergeometric potential …
In this paper an exact transparent boundary condition (TBC) for the multidimensional Schr\"odinger equation in a hyperrectangular computational domain is proposed. It is derived as a generalization of exact transparent boundary conditions…
We study the Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+V\psi$ on $L^2((0,1),\mathbb{C})$ where $V$ is a very high and localized potential wall. We aim to perform permutations of the eigenmodes and to control the solution of the…
We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we…
We investigate the dispersive properties of solutions to the Schr\"odinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schr\"odinger flow on…
We examine the conditions under which the solution of the radial stationary Schr\"odinger equation for the sextic anharmonic oscillator can be expanded in terms of Hermite functions. We find that this is possible for an infinite hierarchy…
We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.
The Schr\"odinger equation with a Lennard-Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer,…
In this paper, we study Schr\"{o}dinger equations on elliptic curves called generalized Lam\'{e} equations. We suggest a method of finding integrable potentials for Schr\"{o}dinger type equations. We apply this method to the Lam\'{e}…
Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…
We examine the one-dimensional quantum dynamics of a Schroedinger particle in a potential represented by a generalized function of the form $U(x) = -\alpha \delta (x) + \beta d(\delta (x))/dx$ superposed on a well behaved potential $V(x)$.…
Oblique propagation of magnetohydrodynamic waves in warm plasmas is described by a modified vector derivative nonlinear Schroedinger equation, if charge separation in Poisson's equation and the displacement current in Ampere's law are…
Nonlocality in the scattering potential leads to an integro-differential equation.In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schroedinger equation is usually handled by…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…
This article deals with two classes of quasi-exactly solvable (QES) trigonometric potentials for which the one-dimensional Schroedinger equation reduces to a confluent Heun equation (CHE) where the independent variable takes only finite…
Analytical solutions are presented for eigenvalues, eigenfunctions of {\color{red} D-dimensional Schrodinger equation having Eckart potential} within Nikiforov-Uvarov method. This uses a new, improved approximation for centrifugal term,…
We present one dimensional potentials $V(x)= V_0[e^{2|x|/a}-1]$ as solvable models of a well $(V_0>0)$ and a barrier ($V_0<0$). Apart from being new addition to solvable models, these models are instructive for finding bound and scattering…