### Abstract

We formulate a theorem saying that the Dirac operator corresponding to a one-electron atomic ion is essentially self-adjoint on the usual domain, provided that the nuclear charge Z is less than 118. Furthermore, for such nuclear charges the domains of the closure of the free particle and total Dirac operators are equal. In the present part I of this paper we prove this theorem for the part of the operator over each of the usual reducing subspaces.

Original language | English (US) |
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Pages (from-to) | 2204-2211 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 20 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1978 |

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## Cite this

Landgren, J. J., & Rejto, P. A. (1978). An application of the maximum principle to the study of essential self-adjointness of Dirac operators. I.

*Journal of Mathematical Physics*,*20*(11), 2204-2211. https://doi.org/10.1063/1.523999