Semiclassical approximations in phase space with coherent states
Semiclassical approximations in phase space with coherent states
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DOI：
10.1088/0305-4470/34/36/309
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发表时间：
2001-09-14
期刊：
影响因子：
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通讯作者：
Schellhaass, B
中科院分区：
文献类型：
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作者：
Baranger, M;de Aguiar, MAM;Schellhaass, B
我们提出了一个完整的推导的相干态传播子在一维的半经典极限，从相空间中的路径积分。我们表明，路径积分表示的任意性，这是从相干态的过完备性，导致许多不同的半经典极限。我们明确推导出两种可能的半经典公式的传播，我们建议第三个，我们讨论了它们之间的关系。我们还推导出一个初始值表示的半经典传播，基于初始高斯波包。它与海勒的解冻高斯近似有关，但又不同。它与赫尔曼-克鲁克公式非常不同，后者不是正确的半经典极限。我们指出了后者的两个推导中的错误。最后，我们展示了如何半经典相干态传播子导致WKB型量子化规则和近似的Husimi分布的定态。
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.