Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent states

TL;DR

This paper introduces a novel approach using unitary transformations to analyze position-dependent mass quantum systems, clarifies operator ordering ambiguities via SUSY symmetry, and constructs coherent states that minimize uncertainty relations.

Contribution

It presents a new method for handling ordering ambiguities in PDM Hamiltonians using SUSY symmetry and constructs coherent states with minimized uncertainty relations.

Findings

Operator ordering ambiguities explained by SUSY symmetry.

Coherent states constructed for PDM Hamiltonians.

States saturate and minimize the GUR under certain conditions.

Abstract

By means of the unitary transformation, a new way for discussing the ordering prescription of Schrodinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter choices in the kinetic part of the Hamiltonian can be explained through an exact SUSY symmetry as well as a consequence of an accidental symmetry under the Z2 action. By making use of the unitary transformation, we construct coherent states for a family of PDM isospectral Hamiltonians from a suitable choice of ladder operators. We show that these states preserve the usual structure of Klauder-Perelomov s states and thus saturate and minimize the generalized position-momentum uncertainty relation (GUR) under some special restrictions. We show that GURs properties can be used to determine the sign of the superpotential.