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

Research output

Abstract

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.
Original languageEnglish
Article number012019
JournalIOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002
Volume1205
Issue number012019
DOIs
Publication statusPublished - 2019

Cite this

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title = "On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators",
abstract = "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.",
author = "Головин, {Александр Викторович} and Lagodinskiy, {Vladimir M.}",
year = "2019",
doi = "10.1088/1742-6596/1205/1/012019",
language = "English",
volume = "1205",
journal = "IOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002",
number = "012019",

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TY - JOUR

T1 - On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators

AU - Головин, Александр Викторович

AU - Lagodinskiy, Vladimir M.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1088/1742-6596/1205/1/012019

DO - 10.1088/1742-6596/1205/1/012019

M3 - Article

VL - 1205

JO - IOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002

JF - IOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002

IS - 012019

M1 - 012019

ER -