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Physica B Condensed Matter

Special treatment of the optical potential of a spherical attractive fermi gas as a Saxon-Woods potential

M. Grado-Caffaro, M. Grado-Caffaro

Published Dec 10, 2014• 0 citations
Publisher
DOI
10.1016/j.physb.2014.12.003

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The one-dimensional Dirac equation with position dependent mass in the generalized asymmetric Woods-Saxon potential is solved in terms of the hypergeometric functions. The transmission and reflection coefficients are obtained by considering the one-dimensional electric current density for the Dirac particle and the equation describing the bound states is found by utilizing the continuity conditions of the obtained wave function. Also, by using the generalized asymmetric Woods-Saxon potential solutions, the scattering states are found out without making calculation for the Woods-Saxon, Hulthen, cusp potentials, and so forth, which are derived from the generalized asymmetric Woods-Saxon potential and the conditions describing transmission resonances and supercriticality are achieved. At the same time, the data obtained in this work are compared with the results achieved in earlier studies and are observed to be consistent.
The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS] potential is derived. The result is shown to be analogous to that of the classical engine and found to agree, within an appropriate limit, with existing results obtained from other potential models. This implies that the [WS] potential can be used as an alternative model in quantum engines.