Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

Al-Hashimi, Munir; Shalaby, A.M.; Wiese, Uwe-Jens (2015). Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity. Annals of physics, 362, pp. 621-641. Elsevier 10.1016/j.aop.2015.08.015

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The 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 γ = 2/R. 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Al-Hashimi, Munir and Wiese, Uwe-Jens

Subjects:

500 Science > 530 Physics

ISSN:

0003-4916

Publisher:

Elsevier

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

24 Sep 2015 09:46

Last Modified:

28 Aug 2017 02:30

Publisher DOI:

10.1016/j.aop.2015.08.015

BORIS DOI:

10.7892/boris.71957

URI:

https://boris.unibe.ch/id/eprint/71957

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