Standard

On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators. / Golovin, A.V.; Lagodinskiy, V. M.

In: Journal of Physics: Conference Series, Vol. 1205, No. 1, 012019, 2019.

Research output: Contribution to journal › Article › peer-review

Harvard

Golovin, AV & Lagodinskiy, VM 2019, 'On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators', Journal of Physics: Conference Series, vol. 1205, no. 1, 012019. https://doi.org/10.1088/1742-6596/1205/1/012019

APA

Golovin, A. V., & Lagodinskiy, V. M. (2019). On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators. Journal of Physics: Conference Series, 1205(1), [012019]. https://doi.org/10.1088/1742-6596/1205/1/012019

Vancouver

Golovin AV, Lagodinskiy VM. On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators. Journal of Physics: Conference Series. 2019;1205(1). 012019. https://doi.org/10.1088/1742-6596/1205/1/012019

Author

Golovin, A.V. ; Lagodinskiy, V. M. / On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators. In: Journal of Physics: Conference Series. 2019 ; Vol. 1205, No. 1.

BibTeX

@article{59c1c1357a0d4354be3dbe5d9435819c,
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{\"o}dinger equation as a close analog of the non-relativistic Schr{\"o}dinger 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 = "A.V. Golovin and Lagodinskiy, {V. M.}",
year = "2019",
doi = "10.1088/1742-6596/1205/1/012019",
language = "English",
volume = "1205",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

RIS

TY - JOUR

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

AU - Golovin, A.V.

AU - Lagodinskiy, V. 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 Schrödinger equation as a close analog of the non-relativistic Schrödinger 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 Schrödinger equation as a close analog of the non-relativistic Schrödinger 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.

UR - http://www.scopus.com/inward/record.url?scp=85066314132&partnerID=8YFLogxK

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

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

M3 - Article

VL - 1205

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012019

ER -

ID: 45257335