Energy levels of a hydrogenic impurity in a parabolic quantum well with a magnetic field

Abstract

In this paper, we present a calculation of the energy levels of a hydrogenic impurity (or a hydrogenic atom) at the bottom of a one-dimensional parabolic quantum well with a magnetic field normal to the plane of the well. The finite-basis-set variational method is used to calculate the ground state and the excited states with major quantum number less than or equal to 3. The limit of small radial distance and the limit of great radial distance are considered to choose a set of proper basis functions. The results in the limit that the parabolic parameter \ensuremath{\alpha}=0 are compared with the data of R\"osner et al. [J. Phys. B 17, 29 (1984)]. The comparison shows that the present calculation is quite accurate. It is found that the energy levels increase with increasing parabolic parameter \ensuremath{\alpha} and increase with increasing normalized magnetic-field strength \ensuremath{\gamma} except those levels with magnetic quantum number m0 at small \ensuremath{\gamma}.