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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 046, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.046
(Mi sigma392)
 

This article is cited in 36 scientific papers (total in 36 papers)

Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

Christiane Quesne

Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
References:
Abstract: On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schrödinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the Schrödinger equation is exactly solvable. This approach has provided the bound-state energy spectrum, as well as the ground-state and the first few excited-state wavefunctions. The general wavefunctions have however remained unknown in explicit form because for their determination one would need the solutions of a rather tricky differential-difference equation. Here we show that solving this equation may be avoided by combining the deformed shape invariance technique with the point canonical transformation method in a novel way. It consists in employing our previous knowledge of the PDM problem energy spectrum to construct a constant-mass Schrödinger equation with similar characteristics and in deducing the PDM wavefunctions from the known constant-mass ones. Finally, the equivalence of the wavefunctions coming from both approaches is checked.
Keywords: Schrödinger equation; position-dependent mass; shape invariance; point canonical transformations.
Received: February 9, 2009; in final form March 19, 2009; Published online April 15, 2009
Bibliographic databases:
Document Type: Article
MSC: 81Q05; 81Q60
Language: English
Citation: Christiane Quesne, “Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations”, SIGMA, 5 (2009), 046, 17 pp.
Citation in format AMSBIB
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\by Christiane Quesne
\paper Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schr\"odinger Equations
\jour SIGMA
\yr 2009
\vol 5
\papernumber 046
\totalpages 17
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  • This publication is cited in the following 36 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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