Generalized Harmonic Oscillator and the Schr\"{o}dinger Equation with Position-Dependent Mass
Quantum Physics
2007-07-24 v1
Abstract
We study the generalized harmonic oscillator which has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and the its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.
Cite
@article{arxiv.0707.3259,
title = {Generalized Harmonic Oscillator and the Schr\"{o}dinger Equation with Position-Dependent Mass},
author = {Ju Guo-Xing and Cai Chang-Ying and Ren Zhong-Zhou},
journal= {arXiv preprint arXiv:0707.3259},
year = {2007}
}
Comments
13 pages