SU(1,1) Coherent States For Position-Dependent Mass Singular Oscillators

TL;DR

This paper solves the Schrödinger equation for position-dependent mass singular oscillators using factorization and transformations, constructing su(1,1) algebra and coherent states, revealing spectral similarities with conventional oscillators.

Contribution

It introduces a method to analyze position-dependent mass oscillators, constructing su(1,1) coherent states and demonstrating their structural preservation.

Findings

Spectrum matches that of the conventional singular oscillator.

Ladder operators form an su(1,1) Lie algebra.

Coherent states are preserved under point transformations.

Abstract

The Schroedinger equation for position-dependent mass singular oscillators is solved by means of the factorization method and point transformations. These systems share their spectrum with the conventional singular oscillator. Ladder operators are constructed to close the su(1,1) Lie algebra and the involved point transformations are shown to preserve the structure of the Barut-Girardello and Perelomov coherent states.