### 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 language | English |
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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

Головин, А. В., & Lagodinskiy, V. M. (2019). On the possibility of constructing relativistic quantum mechanics on the basis of the definition of the functions of differential operators.

*IOP Conf. Series: Journal of Physics: Conf. Series 1124 (2018) 031002*,*1205*(012019), [012019]. https://doi.org/10.1088/1742-6596/1205/1/012019