Semiclassical approximation of functional integrals containing the centrifugal potential
Victor MalyutinInstitute of Mathematics of the National Academy of Sciences of BelarusB. O. NurjanovInstitute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan; Karakalpak State University named after Berdakh
Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Seriesjournal2023en
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In this paper, we consider the class of functional integrals with respect to the conditional Wiener measure, which is important for applications. These integrals are written using the action functional containing terms corresponding to kinetic and potential energies. For the considered class of integrals an approach to semiclassical approximation is developed. This approach is based on the decomposition of the action with respect to the classical trajectory. In the expansion of the action, only terms with degrees zero and two are used. A numerical analysis of the accuracy of the semiclassical approximation for functional integrals containing the centrifugal potential is done.
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