Comparison Theorems for the Position-Dependent Mass Schrödinger Equation
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-12-06
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The following comparison rules for the discrete spectrum of the position-dependent mass (PDM) Schrödinger equation are established.
(i) If a constant mass m0 and a PDM m(x) are ordered everywhere, that is either, m0≤m(x) or m0≥m(x), then the corresponding eigenvalues of the constant-mass Hamiltonian and of the PDM Hamiltonian with the same potential and the BenDaniel-Duke ambiguity parameters are ordered.
(ii) The corresponding eigenvalues of PDM Hamiltonians with the different sets of ambiguity parameters are ordered if ∇2(1/m(x)) has a definite sign.
We prove these statements by using the Hellmann-Feynman theorem and offer examples of their application.
American Psychological Association (APA)
Kulikov, D. A.. 2011. Comparison Theorems for the Position-Dependent Mass Schrödinger Equation. ISRN Mathematical Physics،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-473393
Modern Language Association (MLA)
Kulikov, D. A.. Comparison Theorems for the Position-Dependent Mass Schrödinger Equation. ISRN Mathematical Physics No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-473393
American Medical Association (AMA)
Kulikov, D. A.. Comparison Theorems for the Position-Dependent Mass Schrödinger Equation. ISRN Mathematical Physics. 2011. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-473393
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473393