Consider an electron in a cubic crystal of a semiconductor material. Such an electron is free to move throughout the cubic volume of the crystal, but cannot escape outside the cube. It is trapped in a three-dimensional infinite potential well. The electron can move in three dimensions. The potential function is given by V(x,y,z)=0 for 0 < x < L, 0 < y < 1.5L, and 0 < z < 2L. V(x,y,z)=? elsewhere. Let L = 1.5Å. (Note: 1 Å = 1 x 10-10 m)
(a.) Set up and solve Schrodinger's wave equation for all regions (make sure to apply postulates on ? .
(b.) Find the wave solutions (?(x,y,z) ) for all regions.
(c.) Is this Energy quantized or continuous? Explain why.
(d.) Calculate the energies of the lowest three distinct non-degenerate states.
(e.) Using Matlab, graph the normalized wave solutions (ie. |?(x,y,z)|2) for 0 < x < L and
0 < y < 1.5L and 0 < z < 2L associated with the following energy states:
1) E2,3,1
2) E1,2,2
3) E3,1,3