Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

Abstract

We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner Hamiltonians and the shape invariance technique we obtain the eigenstates and the eigenvalues along with the ladders operators, thus showing a preservation of the supersymmetric structure in terms of the deformed counterpartners. The deformed space in supersymmetry allows to characterize position-dependent effective mass, uniform field interactions and to obtain a generalized uncertainty relation (GUP) that behaves as a distinguishability measure for the coherent states, these latter satisfying a periodic evolution of the GUP corrections.

arXiv comment18 pages, 5 figures

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Cited by in corpus (4)

• Exact solution and coherent states of an asymmetric oscillator with position-dependent mass
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• Dynamics of free time-dependent effective mass
• Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space