广义谐振子与质量依赖于位置的薛定谔方程
Generalized Harmonic Oscillator and the Schrödinger Equation with Position-Dependent Mass
摘要：
在更一般的框架下，研究了具有依赖于位置的质量和依赖于质量函数形式的势的广义谐振子。给出了这类系统的本征值和本征函数的显式表达式，它们与通常的等质量谐振子的本征值和本征函数具有相同的形式。讨论了含PDM系统的相干态及其性质。给出了几种质量函数的有效势，具有这种势的系统与通常的谐振子是等谱的。
英文摘要：
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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