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Journal of the Korean Physical Society

Investigation of the non-relativistic fermi-gas model by considering the position-dependent mass

Soroush Zare, M. de Montigny, HASSAN HASSANABADI

Published Jan 1, 2017• 2 citations
Publisher

Abstract

We investigate the Schrödinger equation in the position-dependent mass framework with an infinite square well potential. We apply this approach to a Fermi gas, calculate the density of states of the gas, examine the information entropy, some expectation values and the uncertainty principle.
DOI
10.3938/jkps.70.122

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The object of this paper is to investigate, classically and quantum mechanically, the relation existing between the position-dependent effective mass and damping–antidamping dynamics. The quantization of the equations of motion is carried out using the geometric interpretation of the motion, and we compare it with the one based on the ordering ambiguity scheme. Furthermore, we apply the obtained results to a Fermi gas of damped–antidamped particles, and solve the Schrödinger equation for an exponentially increasing (decreasing) mass in the presence of the Morse potential.
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This paper presents a detailed analysis of the radial uncertainty product for quantum systems with spherically symmetric potentials. Using the principles of quantum mechanics, the study derives the radial uncertainty relation analogous to the Cartesian form and investigates its implications for three key spherically symmetric potentials: the Hydrogen atom, the infinite spherical potential well, and the spherical harmonic oscillator, all within the non-relativistic regime. Employing the Schrodinger equation in spherical coordinates, the paper rigorously evaluates the normalized radial wave functions, expectation values, and uncertainties associated with both position and momentum. Analytical derivations and numerical computations highlight the dependence of the uncertainty product on quantum numbers and system-specific parameters.