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

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.

Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.

Managing atypical and typical herpetic central nervous system infections: results of a multinational study

There have been many studies pertaining to the management of herpetic meningoencephalitis (HME), but the majority of them have focussed on virologically unconfirmed cases or included only small sample sizes. We have conducted a multicentre study aimed at providing management strategies for HME. Overall, 501 adult patients with PCR-proven HME were included retrospectively from 35 referral centres in 10 countries; 496 patients were found to be eligible for the analysis. Cerebrospinal fluid (CSF) analysis using a PCR assay yielded herpes simplex virus (HSV)-1 DNA in 351 patients (70.8%), HSV-2 DNA in 83 patients (16.7%) and undefined HSV DNA type in 62 patients (12.5%). A total of 379 patients (76.4%) had at least one of the specified characteristics of encephalitis, and we placed these patients into the encephalitis presentation group. The remaining 117 patients (23.6%) had none of these findings, and these patients were placed in the nonencephalitis presentation group. Abnormalities suggestive of encephalitis were detected in magnetic resonance imaging (MRI) in 83.9% of the patients and in electroencephalography (EEG) in 91.0% of patients in the encephalitis presentation group. In the nonencephalitis presentation group, MRI and EEG data were suggestive of encephalitis in 33.3 and 61.9% of patients, respectively. However, the concomitant use of MRI and EEG indicated encephalitis in 96.3 and 87.5% of the cases with and without encephalitic clinical presentation, respectively. Considering the subtle nature of HME, CSF HSV PCR, EEG and MRI data should be collected for all patients with a central nervous system infection.