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arXiv:2508.07228 · East European Journal of Physics

Squeezed Coherent States in Supersymmetric Quantum Mechanics with Position-Dependent Mass

Daniel Sabi Takou, Amidou Boukari, Assimiou Yarou Mora, Gabriel Y. H. Avossevou

Published Dec 8, 2025• 0 citations
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Abstract

In this paper, we construct and analyze a class of squeezed coherent states within the framework of supersymmetric quantum mechanics (SUSYQM) involving a position-dependent mass (PDM). Using a deformed algebraic structure, we generalize the creation and annihilation operators to accommodate spatially varying mass profiles. The resulting states exhibit non-classical features, such as squeezing, coherence, and modified uncertainty relations, strongly influenced by both the deformation parameters and the mass function. We explore their physical properties through expectation values, variances, and probability densities. This work provides a pathway toward extending coherent state theory to more complex quantum systems with geometrical and algebraic richness.

DOI
10.26565/2312-4334-2025-4-06

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The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.
We obtain the Robertson–Schrödinger uncertainty relation for shape-invariant systems and construct generalized Robertson intelligent states for these systems using an algebraic approach based on the supersymmetric quantum mechanics. Using the variances of generalized quadrature operators we study the coherency and squeezing properties, evaluating their dependence on different kinds of generalizations for shape-invariant systems with potential parameters related by a translation (Pöschl–Teller potential) and by a scaling (self-similar potential).
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Generalized coherent states and uncertainty relations in PT\mathcal{P}\mathcal{T}PT-symmetric position dependent mass systems
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