Effective mass Schr?dinger equation with Thomas-Fermi potential

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Ovando, G.^1 ; Peña, J.J.^1 ; Morales, J.^1

Universidad Autónoma Metropolitana-Azcapotzalco, CBI-Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, México, D. F.

02200, Mexico^1

关键词: Bessel functions of the first kind;    Carrier effective mass;    Closed solutions;    Dinger equation;    Exponential type;    Point canonical transformations;    Position-dependent mass;    Thomas-Fermi;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012108/pdf
DOI  :  10.1088/1742-6596/574/1/012108

来源: IOP

【 摘 要 】

The exactly-solvable position-dependent mass Schrodinger equation (PDMSE) for the Thomas-Fermi potential is presented. The PDMSE is transformed into a standard Schrodinger equation (SSE) with constant mass by means of a point canonical transformation scheme. By proposing an exponential type potential of the SSE it is possible to determine a PDMSE with the Thomas-Fermi potential. The resulting PDMSE is carried to the Sturm- Liouville form and the corresponding theory is developed for the particular resulting problem in order to obtain closed solutions in terms of Bessel functions of the first kind. Beyond the case considered in this work, the approach is general and can be useful in the study of electronic properties of non-uniform materials in which the carrier effective mass depends on the position as well as in the search of new solvable potentials suitable for quantum systems.