A solution of the two-dimensional Schrodinger equation

Roman Ya. Kezerashvili, Luo, Jianning, Claudio R. Malvino

Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schrödinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer, and modified Kratzer potentials. We found the exact bound state solutions of the two--dimensional Schrödinger equation with Kratzer--type potentials and present analytical expressions for the eigenvalues and eigenfunctions. The eigenfunctions are given in terms of the associated Laguerre polynomials.

Galina A. Nemova

H. T. Williams

I present a method in the spirit of Green’s functions for generating bound state solutions to the Schrödinger equation. The method is demonstrated by generating ground state and excited state solutions to the one-dimensional, time-independent Schrödinger equation. Its applicability to the radial equation for two and three dimensions is also discussed.

S. Brandt, Hans Dieter Dahmen

S. Brandt, Hans Dieter Dahmen

Glenn F. Webb

The one-dimensional time-dependent complex-valued Schrödinger equation is used to describe the interference diffraction patterns of two-slit experiments in quantum mechanics. The properties of the diffraction patterns are related to the initial data of the Schrödinger equation. The Schrödinger equation solutions are compared to Fraunhofer diffraction formulas in geometric optics, and to the solutions of nonlocal advection diffusion equations.