Radial power-law position-dependent mass; Cylindrical coordinates, separability, and spectral signatures

TL;DR

This paper investigates the separability of the position-dependent mass Hamiltonian in cylindrical coordinates with radial power-law dependence, analyzing spectral signatures for harmonic oscillator and Coulombic mass settings under azimuthal symmetry.

Contribution

It introduces a framework for analyzing the separability of position-dependent mass Hamiltonians with radial power-law dependence in cylindrical coordinates, focusing on harmonic oscillator and Coulombic mass types.

Findings

Spectral signatures vary with different z-dependent potentials.

Separability is achievable under azimuthal symmetry.

Distinct spectral features are identified for harmonic oscillator and Coulombic mass cases.

Abstract

We discuss the separability of the position-dependent mass Hamiltonian in cylindrical coordinates in the framework of a radial power-law position-dependent mass. We consider two particular radial mass settings; a harmonic oscillator type, and a Coulombic type. We subject the radial harmonic oscillator type mass to a radial harmonic oscillator potential and the radial Coulombic mass to a radial Coulombic potential. Azimuthal symmetry is assumed and spectral signatures of various z-dependent interaction potentials are reported.