Pseudo-Hermitian coherent states under the generalized quantum condition with position-dependent mass

TL;DR

This paper explores pseudo-Hermitian and Hermitian coherent states within a position-dependent mass framework, constructing exactly solvable potentials and analyzing their properties through a generalized quantum condition.

Contribution

It introduces a method to construct pseudo-Hermitian and Hermitian coherent states with position-dependent mass using a modified superpotential and ladder operators.

Findings

Constructed a class of exactly solvable potentials.

Established the structure of pseudo-Hermitian coherent states.

Demonstrated minimization of the generalized position-momentum uncertainty.

Abstract

In the context of the factorization method, we investigate the pseudo- Hermitian coherent states and its Hermitian counterpart coherent states under the generalized quantum condition in the framework of a position-dependent mass. By considering a specific modification in the superpotential, a suitable annihilation and creation operators are constructed in order to reproduce the Hermitian counterpart Hamiltonian in the factorized form. We show that by means of these ladder operators we can construct a wide kind of exactly solvable potentials as well as their accompanying coherent states. Alternatively, we explore the relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterparts, obtained from a similarity transformation, to construct the associated pseudo-Hermitian coherent states. These latter preserve the structure of Perelomov's states and minimize the generalized position-momentum uncertainty principal.