Harmonic Oscillator, Coherent States, and Feynman Path Integral
摘要
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be interpreted as the result of a (formal) {\em invariance} under a unitary transformation which relates the same harmonic oscillator. In the path integral formalism, the invariance is reflected in that the kernels do not depend on the choice of classical solutions.
引用
@article{arxiv.quant-ph/0211106,
title = {Harmonic Oscillator, Coherent States, and Feynman Path Integral},
author = {Dae-Yup Song},
journal= {arXiv preprint arXiv:quant-ph/0211106},
year = {2007}
}
备注
Prepared for the Feynman Festival, 23-28 August 2002, University of Maryland College Park, Maryland, U.S.A., and for the Pac Memorial Symposium on Theorectical Physics, 28-29 June 2002, Seoul National University, Seoul, Korea