Electron energies and states at the deep impurity level in a semiconductor

The problem of the model description of the electron state at the deep impurity level in a semiconductor is solved. The potential of the impurity center is chosen as the superposition of a Coulomb field and a spherical quantum well with a flat bottom. The energy level and the wave function of the ground state are determined by the exact method and the variational Ritz method in wide ranges of parameters of the well. An algorithm for determining the energies and wave functions of the first excited states is presented. The advantages of the variational method over the exact solution are demonstrated.