Algebraic approach to non-separable two-dimensional Schrodinger equation: Ground states for polynomial and Morse-like potentials

Abstract

This paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrodinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed.

Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

Keywords

• algebraic methods
• analytical methods
• quantum mechanics