Approximate evaluation of functional integrals generated by the relativistic Hamiltonian
https://doi.org/10.29235/1561-2430-2020-56-1-72-83
Abstract
An approximate evaluation of matrix-valued functional integrals generated by the relativistic Hamiltonian is considered. The method of evaluation of functional integrals is based on the expansion in the eigenfunctions of Hamiltonian generating the functional integral. To find the eigenfunctions and the eigenvalues the initial Hamiltonian is considered as a sum of the unperturbed operator and a small correction to it, and the perturbation theory is used. The eigenvalues and the eigenfunctions of the unperturbed operator are found using the Sturm sequence method and the reverse iteration method. This approach allows one to significantly reduce the computation time and the used computer memory compared to the other known methods.
About the Authors
E. A. Ayryan
Joint Institute for Nuclear Research; RUDN University
Russian Federation
Russian Federation
Edik A. Ayryan – Ph. D. (Physics and Mathematics), Head of Sector, Laboratory of Information Technologies, Joint Institute for Nuclear Research (6, Joliot-Curie Str., 141980, Dubna); RUDN University (6, Miklukho-Maklay Str., 117198, Moscow)
M. Hnatic
Joint Institute for Nuclear Research, Russia; Slovak Academy of Sciences; P. J. Šafárik University
Slovakia
Slovakia
Michal Hnatic – Dr. Sc. (Physics and Mathematics), Deputy Director, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (6, Joliot-Curie Str., 141980, Dubna, Russian Federation); Institute of Experimental Physics of the Slovak Academy of Sciences (IEP SAS) (47, Watsonova Str., 04001, Košice, Slovak Re public); Faculty of Science P. J. Safarik University (9, Park Angelinum, 04001, Košice, Slovak Republic)
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, MinskReferences
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