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Some essentially self-adjoint Dirac type operators i (formulation and an extension of the rellich-kato theorem)

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Abstract

It has been shown by Rellich, Weidman, and Gustafson-Rejto that the one-electron Dirac operator is essentially self-adjoint on the domain of infinitely differentiable functions with compact support, for atomic numbers less than or equal to 118. We state a double perturbation theorem which shows that the one-electron Dirac operator can admit another perturbation in addition to the Coulomb potential, which satisfies a mild Stummel type bound. In addition, the domain of the closure of the perturbed operator is the same as the domain of the closure of the unperturbed operator.

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Abbreviations

√:

square root

<, ≤, >, ≥:

inequalities

∞:

infinity

γ:

gamma

μ:

mu

∂:

partial derivative

Σ:

summation

⊗:

tensor product

||:

absolute value

±:

plus or minus

α:

alpha

→:

limit

ρ:

rho

∩:

intersection

∫:

integral

‖‖:

norm

*:

adjoint

Δ:

Laplacian

ω:

omega

ξ:

xi

η:

eta

1/2:

fraction

∈:

is an element of

⊂:

is a subset of

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Authors and Affiliations

  1. Georgia Institute of Technology, School of Mathematics, 30332, Atlanta, Georgia, U.S.A.

    J. J. Landgren

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  1. J. J. Landgren
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Landgren, J.J. Some essentially self-adjoint Dirac type operators i (formulation and an extension of the rellich-kato theorem). Lett Math Phys 2, 61–70 (1977). https://doi.org/10.1007/BF00420673

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  • DOI: https://doi.org/10.1007/BF00420673

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