On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators

A.V. Golovin, V. M. Lagodinskiy

Результат исследований: Научные публикации в периодических изданияхстатья

Аннотация

A new definition of the function of a differential operator that leads to local operators of infinite order is proposed. It allows one to obtain an expression for the square root of the differential operator (the Hamiltonian of a free spinless particle) and to determine the relativistic Schr¨odinger equation as a close analog of the non-relativistic Schr¨odinger equation. It is shown that this equation does not lead to difficulties of the Klein-Gordon equation. Boundary conditions that lead to self-adjoint boundary problems similar to Sturm-Liouville problems, periodic boundary value problems, and singular boundary value problems are determined. Some problems of relativistic quantum mechanics are solved.
Язык оригиналаанглийский
Номер статьи012019
ЖурналJournal of Physics: Conference Series
Том1205
Номер выпуска1
DOI
СостояниеОпубликовано - 2019

Предметные области Scopus

  • Физика и астрономия (все)

Fingerprint Подробные сведения о темах исследования «On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators». Вместе они формируют уникальный семантический отпечаток (fingerprint).

  • Цитировать