A position-dependent mass model for the Thomas–Fermi potential: Exact solvability and relation to δ-doped semiconductors
- Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary IN 46408 (United States)
- Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Zacatenco, 07738 México D.F. (Mexico)
- Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México D.F. (Mexico)
We consider the Schrödinger equation in the Thomas–Fermi field, a model that has been used for describing electron systems in δ-doped semiconductors. It is shown that the problem becomes exactly-solvable if a particular effective (position-dependent) mass distribution is incorporated. Orthogonal sets of normalizable bound state solutions are constructed in explicit form, and the associated energies are determined. We compare our results with the corresponding findings on the constant-mass problem discussed by Ioriatti (1990) [13]. -- Highlights: ► We introduce an exactly solvable, position-dependent mass model for the Thomas–Fermi potential. ► Orthogonal sets of solutions to our model are constructed in closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study.
- OSTI ID:
- 22220739
- Journal Information:
- Annals of Physics (New York), Vol. 333; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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