Quantization of the 1-D harmonic oscillator with variable mass using the operators $\hat v$ and $\hat p$

TL;DR

This paper explores the quantization of a 1-D harmonic oscillator with variable mass using two different operators, revealing that each approach leads to distinct quantum dynamics.

Contribution

It introduces a consistent method to quantize a variable mass harmonic oscillator using novel operators, highlighting differences in resulting quantum behaviors.

Findings

Different quantization methods yield distinct quantum dynamics.

A Hamiltonian and constant of motion are derived for the variable mass system.

The approach provides new insights into variable mass quantum systems.

Abstract

For the 1-D harmonic oscillator with position depending variable mass, a Hamiltonian and constant of motion are given through a consistent approach. Then, the quantization of this system is carried out using the operator $\hat p$, for the Hamiltonian, and the operator $\hat v$ for the constant of motion. We find that the result of both quantizations brings about different quantum dynamics.