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First correction to the quasiclassical scattering amplitude

A. V. Kuzmenko


Abstract: 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.

Received: 10.03.1977

 English version: Theoretical and Mathematical Physics, 1978, 35:2, 462–466