The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

Journal Article · Thu Dec 23 00:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3537852· OSTI ID:21511337

Morales, J; Ovando, G; Pena, J J ^[1]

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1. Universidad Autonoma Metropolitana-Azcapotzalco, CBI-Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico, D. F. (Mexico)

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

• OSTI ID: 21511337
• Journal Information: AIP Conference Proceedings, Vol. 1323, Issue 1; Conference: Symposium on symmetries in nature in memoriam Marcos Moshinsky, Cuernavaca (Mexico), 7-14 Aug 2010; Other Information: DOI: 10.1063/1.3537852; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALLOYS
CANONICAL TRANSFORMATIONS
EFFECTIVE MASS
EXACT SOLUTIONS
FACTORIZATION
FUNCTIONAL ANALYSIS
HARMONIC OSCILLATORS
MASS DISTRIBUTION
QUANTUM FIELD THEORY
SCHROEDINGER EQUATION
SPECTRA
DIFFERENTIAL EQUATIONS
DISTRIBUTION
EQUATIONS
FIELD THEORIES
MASS
MATHEMATICAL SOLUTIONS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
SPATIAL DISTRIBUTION
TRANSFORMATIONS
WAVE EQUATIONS