Harmonic Oscillator, Coherent States, and Feynman Path Integral

Details Harmonic Oscillator, Coherent States, and Feynman Path Integral Harmonic Oscillator, Coherent States, and Feynman Path Integral

2002-11-18

arxiv.org/abs/quant-ph/0211106v1

Physics

Quantum Physics

Prepared for the Feynman Festival, 23-28 August 2002, University of Maryland College Park, Maryland, U.S.A., and for the Pac M

Scientific paper

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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