(Solved): 3D problem. A quantum dot (QD) has dimensions a,b, and c as shown in figure, a<b<c. Find the ...

3D problem. A quantum dot (QD) has dimensions $\mathrm{a},\mathrm{b}$, and $\mathrm{c}$ as shown in figure, $\mathrm{a}<\mathrm{b}<\mathrm{c}$. Find the available energy states of an electron in the QD (assuming the electron is trapped in the QD, it has no interaction with lattice). a) Find total energy $E$ (in terms of quantum numbers) and corresponding wavefunctions of an electron (start form Schrödinger equation and show all work). b) Calculate the lowest and the second-lowest possible energy $E$ (value). What is the degree of degeneracy of these two energy states? c) Let $a<b=c$, find the lowest and the second-lowest energy. What is the degree of degeneracy for each of the two energy states? d) Let $\mathrm{a}=\mathrm{b}=\mathrm{c}$, what is the lowest and the second-lowest energy? What is the degree of degeneracy for each of the two energy states?