First correction to the quasiclassical scattering amplitude
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 282-288
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We consider the first correction (of order $\hslash$) to the quasiclassical scattering amplitude in nonrelativistic quantum mechanics. When represented by two-loop diagrams, this correction contains twofold integrals. In the present paper, the sum of the contributions of the two-loop diagrams is transformed by means of the classical equations of motion into an expression that contains only a single integral. A characteristic feature of the result is that the integrand does not have singularities at the focal points of the classical trajectory. In the one-dimensional case, the general formula simplifies considerably.
@article{TMF_1978_35_2_a14,
author = {A. V. Kuzmenko},
title = {First correction to the quasiclassical scattering amplitude},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {282--288},
publisher = {mathdoc},
volume = {35},
number = {2},
year = {1978},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a14/}
}
A. V. Kuzmenko. First correction to the quasiclassical scattering amplitude. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 282-288. http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a14/