TY - INPR
A1 - Baranger, Michel
A1 - Aguiar, Marcus A. M. de
A1 - Keck, Frank
A1 - Korsch, Hans-Jürgen
A1 - Schellhaaß, Bernd
T1 - Semiclassical Approximations in Phase Space with Coherent States
N2 - 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.
KW - Coherent State
KW - Phase Space
KW - Husimi
KW - Propagator
KW - Semiclassics
KW - IVR
Y1 - 2001
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1285
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-11943
ER -