Semiclassical approximation of functional integrals
| Autor: | B. O. Nurjanov, V. B. Malyutin |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
010302 applied physics
General Mathematics Numerical analysis 010102 general mathematics General Physics and Astronomy Semiclassical physics Eigenfunction Planck constant 01 natural sciences symbols.namesake Computational Theory and Mathematics 0103 physical sciences symbols 0101 mathematics Hamiltonian (quantum mechanics) Mathematical physics Mathematics |
| Zdroj: | Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series. 56:166-174 |
| ISSN: | 2524-2415 1561-2430 |
| DOI: | 10.29235/1561-2430-2020-56-2-166-174 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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