A position dependent mass Hamiltonian and abstract ladder operators

TL;DR

This paper explores a non-self-adjoint, position-dependent mass Hamiltonian using abstract ladder operators and pseudo-bosonic operators, constructing bi-coherent states with explicit examples.

Contribution

It introduces a novel approach employing abstract ladder operators and pseudo-bosonic operators to analyze non-self-adjoint Hamiltonians with position-dependent mass.

Findings

Pseudo-bosonic operators are crucial in analyzing such Hamiltonians.

Bi-coherent states are constructed for the system.

Explicit examples illustrate the theoretical framework.

Abstract

We consider the Hamiltonian $H$ of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called {\em abstract ladder operators}, in the attempt to find its eigenvalues and eigenvectors. We don't assume that $H$ is self-adjoint, while we focus on the case of a factorizable operator. We show then that pseudo-bosonic operators play a relevant role in this analysis, and we construct bi-coherent states attached to these operators. Explicit examples are discussed.