Generalized Harmonic Oscillator and the Schrödinger Equation with Position-Dependent Mass

Details Generalized Harmonic Oscillator and the Schrödinger Equation with Position-Dependent Mass Generalized Harmonic Oscillator and the Schrödinger Equation with Position-Dependent Mass

2007-07-22

arxiv.org/abs/0707.3259v1

Physics

Quantum Physics

13 pages

Scientific paper

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.

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