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Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski

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arxiv 1403.6900 v1 pith:G2VV64V2 submitted 2014-03-27 math.AP math.SP

Takashi Okaji , Hubert Kalf , Osanobu Yamada This is my paper · ORCID
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We consider spectral problems for many-body Dirac operators mentioned by Derezi\'{n}ski in the IAMP News Bulletin of January 2012. In particular, we derive a representation of the Dirac Coulomb operator for a helium-like ion as a matrix operator of order sixteen. We show that it is essentially self-adjoint (under natural restrictions on the coupling constants), that the essential spectrum of its closure is the whole real line and that it has no eigenvalues.

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    math.AP 2024-12 conditional novelty 7.0 of 10

    A spherical-harmonic reduction turns the spectral stability of one- and bi-frequency solitary waves in the 3D Soler model into radial ODE systems, with bi-frequency waves potentially more stable.

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