Quantum states of a hydrogenic donor impurity in a cubic quantum dot by the finite difference method

The problem of a hydrogenic donor impurity in a cubic quantum dot with finite confinement potential is solved by the finite difference method. The discretized matrix equation needs to be solved for its eigenvalues and eigenfunctions. An algorithm of nonlinear programming is utilized for this problem. The results match references qualitatively in the weak regime, but introduce new problems in the strong and intermediate regimes. & 2008 Elsevier Ltd. All rights reserved.