Quantum Operator Approach Applied to the Position-Dependent Mass Schr?dinger Equation

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Ovando, G.^1 ; Peña, J.J.^1 ; Morales, J.^1

Universidad Autónoma Metropolitana, Área de Física Atómica Molecular Aplicada-CBI, Av. Sn. Pablo 180, Azcapotzalco, 02200 México D.F., Mexico^1

关键词: Constant mass;    Dinger equation;    Harmonic oscillator potential;    Kinetic-energy operator;    Mass distribution;    Position-dependent mass;    Potential Model;    Quantum operators;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012201/pdf
DOI  :  10.1088/1742-6596/490/1/012201

来源: IOP

【 摘 要 】

In this work, the quantum operator approach is applied to both, the position-dependent mass Schrodinger 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.