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AuthorAl-Hashimi, M.H.
AuthorShalaby, A.M.
AuthorWiese, U.-J.
Available date2015-12-29T12:54:36Z
Publication Date2015-11
Publication NameAnnals of Physics
CitationAl-Hashimi M.H., Shalaby A.M., Wiese U.-J., Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity, (2015) Annals of Physics, 362, pp. 621-641.
AbstractThe non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or View the MathML source. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.
SponsorNPRP grant # NPRP 5 - 261-1-054 from the Qatar National Research Fund (a member of the Qatar Foundation)
PublisherElsevier Masson
SubjectAtomic spectrum in spherical cavity
SubjectDirac hydrogen atom
SubjectPauli hydrogen atom
SubjectRobin boundary condition
SubjectSelf adjoint extension parameter
TitleFate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity
Volume Number362

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