Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

TL;DR

This paper explores a deformed quantum oscillator with position-dependent mass using supersymmetric formalism, deriving eigenstates, eigenvalues, and coherent states, and analyzing their properties and generalized uncertainty relations.

Contribution

It introduces a supersymmetric approach to a deformed oscillator with position-dependent mass, extending shape invariance and coherent state analysis to this context.

Findings

Eigenstates and eigenvalues derived via shape invariance

Preservation of supersymmetric structure in deformed systems

Generalized uncertainty relation as a distinguishability measure

Abstract

We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner Hamiltonians and the shape invariance technique we obtain the eigenstates and the eigenvalues along with the ladders operators, thus showing a preservation of the supersymmetric structure in terms of the deformed counterpartners. The deformed space in supersymmetry allows to characterize position-dependent effective mass, uniform field interactions and to obtain a generalized uncertainty relation (GUP) that behaves as a distinguishability measure for the coherent states, these latter satisfying a periodic evolution of the GUP corrections.