Variational approach to the soft-Coulomb potential in low-dimensional quantum systems

The variational method is used to obtain the ground-and first-excited states for the soft-Coulomb central potential, 1/root r(2) + d(2), characterized by a bias distance d, taken into account as a fixed parameter. Applications are presented for spatially indirect excitons, i.e., photo-generated electronhole (e-h) bound pairs, where the two charges are kept separated in two different regions of a heterostructure. We consider one-or two-dimensional systems, namely, quantum wires or wells, respectively, and compare the results with numerical calculations obtained by finite-difference diagonalization of the Hamiltonian. An explicit example is given for GaAs-based heterostructures. (C) 2017 American Association of Physics Teachers.