Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

TL;DR

This paper constructs a dynamical symmetry algebra for a semiconfined harmonic oscillator with a position-dependent mass, revealing an $rak{su}(1,1)$ structure and connecting it to the classical harmonic oscillator algebra.

Contribution

It introduces a new algebraic framework for a semiconfined oscillator with variable mass, extending the understanding of its symmetry properties.

Findings

Identified an $rak{su}(1,1)$ algebra for the model

Derived limit relations to the standard harmonic oscillator algebra

Discussed special cases and algebraic limits

Abstract

Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we have found three basis elements of this algebra. The algebra defined through those basis elements is a $\mathfrak{su}\left(1,1 \right)$ Heisenberg-Lie algebra. Different special cases and the limit relations from the basis elements to the Heisenberg-Weyl algebra of the non-relativistic quantum harmonic oscillator are discussed, too.