Semiclassical approximation of functional integrals
https://doi.org/10.29235/1561-2430-2020-56-2-166-174
Abstract
In this paper, we consider a semiclassical approximation of special functional integrals with respect to the conditional Wiener measure. In this apptoximation we use the expansion of the action with respect to the classical trajectory. In so doing, the first three terms of expansion are taken into account. Semiclassical approximation may be interpreted as an expansion in powers of the Planck constant. The novelty of this work is the numerical analysis of the accuracy of the semiclassical approximation of functional integrals. A comparison of the results is used for numerical analysis. Some results are obtained by means of semiclassical approximation, while the other by means of the functional integrals calculation method based on the expansion in eigenfunctions of the Hamiltonian generating a functional integral.
About the Authors
V. B. Malyutin
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Victor B. Malyutin – Dr. Sc. (Physics and Mathematics), Principal Researcher
11, Surganov Str., 220072, Minsk
B. O. Nurjanov
Karakalpak State University named after Berdakh
Uzbekistan
Uzbekistan
Berdakh O. Nurjanov – Ph. D. (Physics and Mathematics), Assistant Professor,
1, Ch. Abdirov Str., 230112, Nukus
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