Binding energy of a hydrogenic donor and of a Wannier exciton in the ‖z${\mathrm{\Vert }}^{2/3}$ quantum well

We have calculated variationally the binding energy of a hydrogenic donor and a Wannier exciton in a quantum well with a potential shape proportional to ‖z${\mathrm{\Vert }}^{2/3}$ as a function of well width and barrier height. The exciton binding energy compares favorably with the experimental result of Sputz and Gossard. A comparison of the results relating to a rectangular well and those of the ‖z${\mathrm{\Vert }}^{2/3}$ well is also presented.