Open AccessApproximate evaluation of the functional integrals generated by the Dirac equation with pseudospin symmetry
Author(s) -
Е. A. Ayryan,
Michal Hnatič,
V. В. Malyutin
Publication year - 2021
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2021-57-1-14-22
Subject(s) - eigenfunction , mathematical physics , hamiltonian (control theory) , eigenvalues and eigenvectors , dirac operator , scalar (mathematics) , dirac equation , momentum operator , mathematics , physics , mathematical analysis , quantum mechanics , ladder operator , compact operator , mathematical optimization , extension (predicate logic) , geometry , computer science , programming language
In this paper, the matrix-valued functional integrals generated by the Dirac equation with relativistic Hamiltonian are considered. The Dirac Hamiltonian contains scalar and vector potentials. The sum of the scalar and vector potentials is equal to zero, i.e., the case of pseudospin symmetry is investigated. In this case, a Schrödinger-type equation for the eigenvalues and eigenfunctions of the relativistic Hamiltonian generating the functional integral is constructed. The eigenvalues and eigenfunctions of the Schrödinger-type operator are found using the Sturm sequence method and the reverse iteration method. A method for the evaluation of matrix-valued functional integrals is proposed. This method is based on the relation between the functional integral and the kernel of the evolution operator with the relativistic Hamiltonian and the expansion of the kernel of the evolution operator in terms of the found eigenfunctions of the relativistic Hamiltonian.