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Semiclassical Approximations in Phase Space with Coherent States

  • We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman - Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

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Author:Michel Baranger, Marcus A. M. de Aguiar, Frank Keck, Hans-Jürgen Korsch, Bernd Schellhaaß
Document Type:Preprint
Language of publication:English
Year of Completion:2001
Year of Publication:2001
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2001/05/31
Tag:Coherent State; Husimi; IVR; Phase Space; Propagator; Semiclassics
Faculties / Organisational entities:Fachbereich Physik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 530 Physik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011