Exact solutions for hydrogenic donor states in a spherically rectangular quantum well

Using different series forms in different regions of the radial equation, we have obtained exact solutions of donor states in a spherically rectangular quantum well by a numerical method. The calculated results show that there are stronger confinement and larger binding energy for a hydrogenic donor in the well of GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As than in quantum-well wires and two-dimensional quantum-well structures.