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

By Yamen Hamdouni

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 Schr\"odinger equation for an exponentially increasing (decreasing) mass in the presence of the Morse potential.Comment: 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 Theoretica

Topics: Quantum Physics, Condensed Matter - Quantum Gases, Physics - Atomic Physics
Year: 2011
DOI identifier: 10.1088/1751-8113/44/38/385301
OAI identifier: oai:arXiv.org:1103.5440
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