On the construction of coherent states of position dependent mass Schr\"odinger equation endowed with effective potential

TL;DR

This paper presents a new algorithm for constructing coherent states in position-dependent mass Schrödinger equations, using point canonical transformations and deformed operators, with applications to novel examples.

Contribution

The authors develop a systematic method to generate coherent states for position-dependent mass systems, including explicit superpotential expressions and uncertainty relations, with new examples provided.

Findings

Deformed ladder operators satisfy minimum uncertainty relations.

Explicit superpotential expressions derived from mass distribution.

New coherent states constructed for specific position-dependent mass systems.

Abstract

In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schr\"odinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schr\"odinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples in which the coherent states given for the second example is new.