Motion of position-dependent mass as a damping-antidamping process: Application to the Fermi gas and to the Morse potential

Abstract

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 we solve the Schrödinger equation for an exponentially increasing (decreasing) mass in the presence of the Morse potential.

Preprint, 24 pages, 2 figures. We now derive the correct condition that should be satisfied by the derivative of the wave function at the discontinuity point and show that the reflexion coefficient is independent of $\eta$. Figure 1 and the corresponding discussion have been removed. Two references added. To be published in Journal of Physics A: Mathematical and Theoretical

References in corpus (7)

• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Deformed algebras, position-dependent effective masses and curved spaces: An exactly solvable Coulomb problem
• Exact solvability of potentials with spatially dependent effective masses
• Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
• Exact solutions of effective-mass Schrodinger equations
• Nonrelativistic Green's function for systems with position-dependent mass
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Cited by in corpus (2)

• Analytic results in the position-dependent mass Schrodinger problem
• Classical and quantum quasi-free position dependent mass; Pöschl-Teller and ordering-ambiguity