Motion of position-dependent mass as a damping-antidamping process: Application to the Fermi gas and to the Morse potential

TL;DR

This paper explores the relationship between position-dependent mass and damping-antidamping dynamics, quantizes the system, and applies the findings to a Fermi gas and Morse potential scenarios.

Contribution

It introduces a geometric quantization approach for position-dependent mass systems and applies it to quantum models like the Fermi gas and Morse potential.

Findings

Established a link between position-dependent mass and damping-antidamping dynamics.

Quantized the equations of motion using geometric interpretation.

Solved Schrödinger equation for specific mass variations in Morse potential.

Abstract

The object of this paper is to investigate, classically and quantum mechanically, the relation existing between the position-dependent effective mass and damping-antidamping dynamics. The quantization of the equations of motion is carried out using the geometric interpretation of the motion, and we compare it with the one based on the ordering ambiguity scheme. Furthermore, we apply the obtained results to a Fermi gas of damped-antidamped particles, and we solve the Schr\"odinger equation for an exponentially increasing (decreasing) mass in the presence of the Morse potential.