Classification of quantum systems with position-dependent effective mass based on lie algebra and special functions
Department of Physics, Faculty of Basic Sciences, Shahed University, Tehran, Iran
Accepted: 30 July 2022
Published online: 17 August 2022
Considering the position-dependent effective mass in the study of quantum mechanical systems, a wide range of solvable potentials has been obtained. These potentials are obtained by applying canonical transformations to the Schrödinger equation. In this method, the internal functions introduced by Levai for solvable potentials with constant mass have been used, and the eigenfunctions and eigenvalues have been fully obtained. The eigenfunction of these solvable potentials can be obtained based on orthogonal polynomials (Jacobian, generalized Laguerre and Hermite polynomials). Some of these potentials are Scarf-II, Pöschl-Teller, Rosen-Mörse-II and Eckart, whose applications have been described in physical systems. Finally, all the results are placed in a table and the figures of the desired functions are drawn for specific values.
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