The energy spectrum for an electron in quantum well wires with different shapes under the electric and magnetic fields

The ground-state energies and wave functions for an electron in quantum well-wires (QWWs) with different shapes under the electric and magnetic fields are directly calculated using the finite difference method. It is shown that the method is able to calculate all energy states for any given QWW shape. Then, the ground-state binding energy of a hydrogenic impurity is found employing a variational method. The reliability of the results is tested against previous studies. The binding energy for QWWs consisting of the combinations of square and triangular well potential is obtained.