Open AccessApproximate evaluation of functional integrals generated by the relativistic Hamiltonian
Author(s) -
Е. A. Ayryan,
Michal Hnatič,
Victor Malyutin
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 - 10.29235/1561-2430-2020-56-1-72-83
Subject(s) - eigenfunction , eigenvalues and eigenvectors , hamiltonian (control theory) , computation , mathematics , mathematical analysis , hamiltonian matrix , perturbation (astronomy) , operator (biology) , mathematical physics , physics , quantum mechanics , symmetric matrix , algorithm , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene
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.