Analytical Solution of Two-Dimensional Scarf II Model by Means of SUSY Methods

TL;DR

This paper introduces an analytical solution for a new two-dimensional quantum model, generalizing the Scarf II potential, using supersymmetrical separation methods, and provides explicit energy levels and wave functions.

Contribution

It presents the first analytical solution to a two-dimensional generalization of the Scarf II model using SUSY quantum mechanics techniques.

Findings

All bound state energies were determined.

Explicit wave functions for bound states were derived.

The model is solvable despite not allowing separation of variables.

Abstract

New two-dimensional quantum model - the generalization of the Scarf II - is completely solved analytically for the integer values of parameter. This model being not amenable to conventional procedure of separation of variables is solved by recently proposed method of supersymmetrical separation. The latter is based on two constituents of SUSY Quantum Mechanics: the intertwining relations with second order supercharges and the property of shape invariance. As a result, all energies of bound states were found, and the analytical expressions for corresponding wave functions were obtained.