Group analysis of Schroedinger equation with generalised Kratzer type potential

TL;DR

This paper employs algebraic methods to analyze the one-dimensional Schrödinger equation with a generalized Kratzer potential, revealing symmetry enhancements and algebraic structures affecting eigenvalues.

Contribution

It introduces a group-theoretic approach using $su(1,1)$ algebra to analyze the Schrödinger equation with a generalized Kratzer potential, highlighting symmetry enhancements.

Findings

Symmetry enhancement occurs at specific parameter values.

The Lie algebra generators do not close, indicating a complex algebraic structure.

The method identifies potentials with similar eigenvalues.

Abstract

Using the method of $su(1,1)$ spectrum generating algebra, we analyze one dimensional Schroedinger equation with potential in the form ${C\over{x^2} + {D\over{x}}$ to obtain a class of potentials giving similar eigenvalues. By a group analysis of the differential equation it is found that the symmetry gets enhanced for particular values of $C$ and $D$. The generators of the Lie algebra do not close. The extension of the vector field gives rise to an interesting algebra.