Position-dependent mass schrödinger equations allowing Harmonic Oscillator (HO) eigenvalues

J. J. Pena, G. Ovando, J. Morales, J. García-Ravelo, C. Pacheco-García

Research output: Contribution to conferencePaper

7 Citations (Scopus)

Abstract

Quantum chemical systems with a position-dependent mass have attracted the attention due to their relevance in describing the features of many microstructures of current interest. In this work, the point canonical transformation method applied to Schrödinger equations with a position-dependent mass (SEPDM) is presented. Essentially, the proposal is aimed to transform the Schrödinger equation with a position-dependent mass into a standard Schrödinger-like equation for constant mass in such a way that the position-dependent mass distribution (PDMD) becomes incorporated into the effective potential. As an useful application of the proposal, it is considered as effective potential the one-dimensional harmonic oscillator potential model, which leads to those isospectral potentials related to different forms of PDMD. For example, the exactly solvable isospectral potentials involved in the SEPDM for some PDMD such as 2m(x) = e-α2x2, 1/(α 2x2 + 1), exp(2αx)/ cosh2(αx), 1/ cos2(αx), exp(-α|x|), xα, and 1/b 2 (b+α2x2/1+α2x 2)2, worked out explicitly including their raising and lowering operators that factorize the SEPDM for each PDMD allowing HO eigenvalues. However, the proposal is general and can be straightforwardly applied to other effective potential models as well as other PDMD that could be useful in quantum chemical applications. © 2008 Wiley Periodicals, Inc.
Original languageAmerican English
Pages2906-2913
Number of pages2614
DOIs
StatePublished - 10 Nov 2008
EventInternational Journal of Quantum Chemistry -
Duration: 1 Jan 2012 → …

Conference

ConferenceInternational Journal of Quantum Chemistry
Period1/01/12 → …

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harmonic oscillators
eigenvalues
mass distribution
Microstructure
proposals
operators
microstructure

Cite this

Pena, J. J., Ovando, G., Morales, J., García-Ravelo, J., & Pacheco-García, C. (2008). Position-dependent mass schrödinger equations allowing Harmonic Oscillator (HO) eigenvalues. 2906-2913. Paper presented at International Journal of Quantum Chemistry, . https://doi.org/10.1002/qua.21879
Pena, J. J. ; Ovando, G. ; Morales, J. ; García-Ravelo, J. ; Pacheco-García, C. / Position-dependent mass schrödinger equations allowing Harmonic Oscillator (HO) eigenvalues. Paper presented at International Journal of Quantum Chemistry, .2614 p.
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Pena, JJ, Ovando, G, Morales, J, García-Ravelo, J & Pacheco-García, C 2008, 'Position-dependent mass schrödinger equations allowing Harmonic Oscillator (HO) eigenvalues', Paper presented at International Journal of Quantum Chemistry, 1/01/12 pp. 2906-2913. https://doi.org/10.1002/qua.21879

Position-dependent mass schrödinger equations allowing Harmonic Oscillator (HO) eigenvalues. / Pena, J. J.; Ovando, G.; Morales, J.; García-Ravelo, J.; Pacheco-García, C.

2008. 2906-2913 Paper presented at International Journal of Quantum Chemistry, .

Research output: Contribution to conferencePaper

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Pena JJ, Ovando G, Morales J, García-Ravelo J, Pacheco-García C. Position-dependent mass schrödinger equations allowing Harmonic Oscillator (HO) eigenvalues. 2008. Paper presented at International Journal of Quantum Chemistry, . https://doi.org/10.1002/qua.21879