par Quesne, Christiane
Référence Journal of Physics A: General Physics, 19, 7, page (1127-1139), 015
Publication Publié, 1986
Article révisé par les pairs
Résumé : The problem of an electron in a general central potential, subject to a constant external magnetic field, is known to have no degeneracy and to be invariant under SO(2). However, once the central potential has a symmetry group larger than SO(3), even in the presence of a magnetic field, residual accidental degeneracies may remain and a symmetry group larger than SO(2) may exist. In the present paper, we investigate the case where the central potential is a harmonic oscillator and the magnetic field is strong, meaning that the Hamiltonian contains both a linear and a quadratic term in the magnetic field intensity H. In a recent work, Moshinsky et al did claim that in such a case no accidental degeneracy is left. It is shown here that, although this assertion is valid for most values of H, there exist values for which there are residual accidental degeneracies. The analysis is based on a linear canonical transformation converting the Hamiltonian into that of an anisotropic oscillator in the absence of magnetic field. It is shown that the accidental degeneracies of the latter are either due to an SU(2), an SU(3) or an SU(2)×SU(2) symmetry group, or cannot be explained by the existence of any symmetry group. In particular, it is proved that accidental degeneracies, and a corresponding SU(2) symmetry group, may appear when the frequencies are irrationally related. Finally the accidental degeneracies and the associated symmetry group of the isotropic oscillator in a strong magnetic field (when it exists) are determined in terms of the ratio between the oscillator and cyclotron frequencies. © 1986 The Institute of Physics.