Semiclassical Approximation

Eugeni P. Gordov, Stanislav D. Tvorogov

A complete orthonormal set of eigenfunctions of the vector-potential operator is introduced. It is shown that the semiclassical approximation is naturally determined in the basis of the functions introduced. The extraction of the semiclassical approximation from nonrelativistic quantum electrodynamics allows the determination of the limits of applicability of the semiclassical approach. It is shown that the semiclassical approximation is inapplicable at sufficiently large photon densities. The advantages of using our set of eigenfunctions for the description of the interaction of a strong quantized field with a quantum system are discussed.

Zhuangqi Cao, Cheng Yin

John R. Klauder

The usual configuration-space semiclassical approximation to wave equations (e.g., Schr\"odinger's equation) needs refinement at caustics. When expressed in a phase-space coherent-state representation, such equations admit a semiclassical solution that properly captures the effects of caustics. Transformation of this expression to the configuration-space representation yields a global, uniform, semiclassical approximation.

Giovanni Di Liberto, Michele Ceotto

Overview• A brief remind about the nature of the semiclassical prefactor.• The problems of the semiclassical prefactor.• Overview of the existing approximations.• Derivation of a new class of prefactor approximations.• Numerical test on chaotic potentials.

Lee E. Estes, Thomas H. Keil, Lorenzo M. Narducci