Open AccessSemiclassical approximation of functional integrals
Author(s) -
Victor Malyutin,
B. O. Nurjanov
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-2-166-174
Subject(s) - semiclassical physics , eigenfunction , mathematics , asymptotic expansion , hamiltonian (control theory) , action (physics) , mathematical analysis , mathematical physics , physics , quantum mechanics , eigenvalues and eigenvectors , mathematical optimization , quantum
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.