Position Dependent Mass Oscillators and Coherent States

TL;DR

This paper explores methods to solve the Schrödinger equation for systems with position-dependent mass, deriving spectra and constructing coherent states that resemble Glauber states, advancing understanding of quantum oscillators with variable mass.

Contribution

It introduces two approaches for analyzing position-dependent mass quantum systems and constructs coherent states maintaining Glauber state structure.

Findings

Derived interaction conditions for specific energy spectra.

Calculated spectra for various mass oscillators.

Constructed coherent states with Glauber-like structure.

Abstract

The solving of the Schrodinger equation for a position-dependent mass quantum system is studied in two ways. First, it is found the interaction which must be applied on a mass m(x) in order to supply it with a particular spectrum of energies. Second, given a specific potential V(x) acting on the mass m(x), the related spectrum is found. The method of solution is applied to a wide class of position-dependent mass oscillators and the corresponding coherent states are constructed. The analytical expressions of such position-dependent mass coherent states preserve the functional structure of the Glauber states.