Iranian Journal of Physics Research

Quantum mechanics solvable systems with position-dependent effective mass

Document Type : Original Article

Authors

Zahra Bakhshi 1
Zahra Bakhshi 2

1 Physics Department, Faculty of Basic Sciences, Shahed University, Tehran, Iran

2 Physics Department, Faculty of Basic Sciences, Shahed University, Tehran

https://doi.org/10.47176/ijpr.22.2.81297
Abstract
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 specific known functions (Jacobian, generalized Laguerre, and Hermit 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 is drawn for specific values

Keywords

position-dependent effective mass
solvable potential
canonical transformations
Schrödinger equation
Subjects
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