In The V-groove Quantum Wire Electron And Hole States

Owing to the easy fabrication and clean, sharp interfaces of V-groove quantum wires, there is great potential application in it. And more attention was paid to it. A simplified effective potential proposed by Geraldo Creci and Gerald weber~[1] is used together with a suitable coordinate transformation proposed by Inoshita T. and Sakaki H.~[2] to deduce two decoupled one-dimensional Schrodinger equations ,which made the problem solved easily . And the results calculated by this method are in agreement with previous results.Whereas the notable merit of this simplified effective potential, we have studied the method deeply.For calculating the physical quantities in quantum wires, it is important to choose a good effective potential model. To choose a reasonable modal, the reduce of the calculation amount and it's physical effective should be taken into account, as for V-groove quantum wires, it is obviouivs that the confinement comes from X-direction and Y-direction at the same time in order to keep agreement with facts.Geraldo Creci and Gerald Weber's effective potential simulates the physical effect of a lateral confinement in the X-direction. And their results of energy and wave function is agree with the results published before, which shows the reasonable of their modal. But when we consider about the confinement in the Y -direction, a better effective potential is in need on the base of its idea. Its accuracy and deficiency is tested in this paper. Moreover, a numerical result for effective potential is abtained, and a trial analytical expression is proposed.In this work, the accuracy of the energy level and wave function calculated by Gerald's lateral effective potential is tested by means of expanding the wave function of election by the eigen function of two -dimensional harmonic oscillator to solve the secular equation. We find that Geraldo's results are in general agreement with our results when the expansion terms are less, but different when the expansion terms are more. We know that the results are nearer to the reality when the expansion terms are more. So Geraldo's effective potential is not accuracy enough. This is mainly because...