Comparison of effective potential method and Rayleigh-Ritz method for the calculation of energy levels of quantum wires

We calculated the electronic energy levels of quantum wires with rectangula r crosssection by two methods, effective potential method and Rayleigh-Ritz method. We compared the performance of these two methods by calculating th e conduction band energy levels of GaAs/Al0.3Ga0.7As quantum wires. The res ults of the two methods agree well when the energy eigenvalues measured fro m the bandedge of the well material are much less than the bandedge energy difference between the well and barrier materials. This observation is cons istent with the expectation that the effective potential method gives accur ate eigenvalues for well confined states. Also the results agree better whe n the aspect ratio of a quantum wire is larger.