Harmonic Oscillator, Coherent States, and Feynman Path Integral

2002/11/18 by Dae-Yup Song, Song, Dae-Yup
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0211106

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

arxiv created 2002/11/18 · openalex publication_date 2002/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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