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

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.

9 pages, 1 figure