Quantum Operator Approach Applied to the Position-Dependent Mass Schrödinger Equation

In this work, the quantum operator approach is applied to both, the position-dependent mass Schrödinger equation (PDMSE) and the Schrodinger equation with constant mass (CMSE). This fact enable us to find the factorization operators that relates both Hamiltonians by means of a kinetic energy operato...

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Bibliographic Details
Published in:Journal of physics. Conference series 2014-01, Vol.490 (1), p.12201-5
Main Authors: Ovando, G, Peña, J J, Morales, J
Format: Article
Language:English
Subjects:
Cases (containers)
Constants
Factorization
Harmonic oscillators
Kinetic energy
Mass distribution
Operators
Physics
Proposals
Schrodinger equation
Schroedinger equation
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Summary:In this work, the quantum operator approach is applied to both, the position-dependent mass Schrödinger equation (PDMSE) and the Schrodinger equation with constant mass (CMSE). This fact enable us to find the factorization operators that relates both Hamiltonians by means of a kinetic energy operator that comes from the proposal of Morrow and Brownstein. With this approach is possible to find the exactly-solvable PDMSE, for any value of the parameters α and γ in the von Roos's Hamiltonian. For that, our proposal can be considered as a unified treatment of the PDMSE because it contains as particular cases, the kinetic energy operators of various authors such as BenDaniel-Duke, Gora-Williams, Zhu-Kroemer and Li-Kuhn among others. To show the usefulness of our result, we show the solvable PDMSE that comes from the harmonic oscillator potential model for the CMSE. The proposal is general and can easily be extended to other potential models and mass distributions which will be given in the extended paper.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/490/1/012201