Semiclassical trajectory-coherent approximation in quantum mechanics. I. High-order corrections to multidimensional time-dependent equations of Schr{umlt o}dinger type

Journal Article · Fri Mar 01 00:00:00 EST 1996 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1996.0027· OSTI ID:284233

Bagrov, V G ^[1]; Belov, V V ^[2]; Trifonov, A Y ^[1]

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1. High-Current Electronics Institute, Siberian Division, Russian Academy of Sciences, 4 Academichesky pr., 634055 Tomsk (Russia)
2. Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, 3/12 B. Vusovsky per., 109028 Moscow (Russia)

A concept of semiclassically concentrated states is developed on the basis of the Maslov germ theory. Higher approximations of semiclassical trajectory-coherent states and of semiclassical Green function (in the class of semiclassically concentrated states) for a many-dimensional Schr{umlt o}dinger-type equation are constructed. It is shown that, in class of such semiclassically concentrated states, a Schr{umlt o}dinger-type equation (up to any order of {h_bar}, {h_bar}{r_arrow}0) is equivalent, from the viewpoint of calculating the quantum averages, to a closed finite system of ordinary differential equations. Copyright {copyright} 1996 Academic Press, Inc.

• OSTI ID: 284233
• Journal Information: Annals of Physics (New York), Vol. 246, Issue 2; Other Information: PBD: Mar 1996
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION
SCHROEDINGER EQUATION
CAUCHY PROBLEM
GREEN FUNCTION
TRAJECTORIES
ASYMPTOTIC SOLUTIONS