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

	Text AnnalsPhys.362.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (1MB) | Request a copy
Preview	Text manuscript.pdf - Accepted Version Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND). Download (1MB) | Preview

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.

Interest & Impact

Downloads

186 since deposited on 24 Sep 2015
24 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item