Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetry

TL;DR

This paper derives the kinetic energy operator for position-dependent mass in cylindrical coordinates, explores the Schrödinger equation's separability under azimuthal symmetry, and analyzes spectral properties of various z-dependent potentials, including PT-symmetric cases.

Contribution

It provides a new form of the kinetic energy operator in cylindrical coordinates with position-dependent mass and investigates the spectral effects of different z-dependent potentials, including PT-symmetric ones.

Findings

Kinetic energy operator for position-dependent mass in cylindrical coordinates derived.

Schrödinger equation separability conditions discussed under azimuthal symmetry.

Spectral signatures of Hermitian and PT-symmetric potentials analyzed.

Abstract

The kinetic energy operator with position-dependent-mass in cylindrical coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed within radial cylindrical mass settings. Azimuthal symmetry is assumed and spectral signatures of various z-dependent interaction potentials (Hermitian and non-Hermitian PT-symmetric) are reported.