Variational calculations of energy levels associated with 1s, 2p and 3d states of hydrogenic donors for semiconductors in arbitrary magnetic field

Abstract

The energies of 1s, 2p −1, 2p 0, 2p +1, 3d −2,3d −1, 3d +2 and 3d +1 states for an isolated hydrogenic donor in single-valley semiconductors are calculated as functions of magnetic field by use of the variational principle. We employ the variational wave functions which are applicable to an arbitrary magnetic field strength. At the low and high magnetic field limits, these variational wave functions become equal to the hydrogen and harmonic-oscillator types. Analytic expressions for the expectation values of the energies are presented according to the variational wave functions which we employ. The binding energy is also calculated as a function of magnetic field. It is found that our present calculations show reliable results in an arbitrary magnetic field.