### Abstract

Original language | English |
---|---|

Article number | 012019 |

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

Volume | 1205 |

Issue number | 012019 |

DOIs | |

Publication status | Published - 2019 |

### Cite this

*IOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002*,

*1205*(012019), [012019]. https://doi.org/10.1088/1742-6596/1205/1/012019

}

*IOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002*, vol. 1205, no. 012019, 012019. https://doi.org/10.1088/1742-6596/1205/1/012019

**On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators.** / Головин, Александр Викторович; Lagodinskiy, Vladimir M.

Research output

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 -