Probability density correlation for PDM-Hamiltonians and superstatistical PDM-partition functions

Schrödinger equation with position-dependent mass (PDM) allows the identification of quantum wave functions in a complex environment. Following the progress of this investigation field, in this work, we consider the non-Hermitian kinetic operators associated with the PDM Schrödinger equation. We pro...

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Bibliographic Details
Published in:European physical journal plus 2021-01, Vol.136 (1), p.96, Article 96
Main Authors: dos Santos, Maike A. F., Gomez, Ignacio S., da Costa, Bruno G., Mustafa, Omar
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Confining
Energy
Exact solutions
Hamiltonian functions
Harmonic oscillators
Inhomogeneity
Mathematical and Computational Physics
Molecular
Operators (mathematics)
Optical and Plasma Physics
Partitions (mathematics)
Physics
Physics and Astronomy
Probability distribution functions
Quantum physics
Regular Article
Schrodinger equation
Semiconductors
Sine waves
Theoretical
Wave functions
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Summary:Schrödinger equation with position-dependent mass (PDM) allows the identification of quantum wave functions in a complex environment. Following the progress of this investigation field, in this work, we consider the non-Hermitian kinetic operators associated with the PDM Schrödinger equation. We provide a simplified picture for PDM quantum systems that admit exact solutions in confining potentials. First, we investigate the solutions for a sinusoidal and an exponential PDM distributions in an infinite potential well. Next, we consider the solutions for a PDM harmonic oscillator potential associated with a power-law PDM distribution. The results presented in this work offer a way to approach new classes of solutions for PDM quantum systems in confining potential (bound states). Complementarily, we interpret the quantum partition function of the canonical ensemble of a PDM system in the context of the superstatistics, which, in turn, allows us to express the inhomogeneity of the PDM in terms of beta distribution f ( β ) , Dirac delta distributions for f ( β ) , and effective temperatures. Our results are, hereby, reported for the sinusoidal and the exponential PDM distributions.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-021-01088-6