Oscillator Algebra in Complex Position-Dependent Mass Systems

TL;DR

This paper develops a systematic method to construct exactly solvable quantum models with complex ladder operators and real spectra in position-dependent mass systems, using algebraic constraints to derive potentials and eigenfunctions.

Contribution

It introduces a new algebraic approach to design exactly solvable models with complex Hamiltonians and real spectra for arbitrary mass profiles.

Findings

Derived potentials and eigenfunctions for specific mass functions.

Established a systematic procedure for constructing solvable models.

Demonstrated models with quadratic, cosenoidal, and exponential mass profiles.

Abstract

This work introduces non-Hermitian position-dependent mass Hamiltonians characterized by complex ladder operators and real, equidistant spectra. By imposing the Heisenberg-Weyl algebraic structure as a constraint, we derive the corresponding potentials, ladder operators, and eigenfunctions. The method provides a systematic procedure for constructing exactly solvable models for arbitrary mass profiles. Specific cases are illustrated for quadratic, cosenoidal, and exponential mass functions.