(a) What are the energy levels and eigenfunctions of a 3D infinite square well for a particle of mass m in (1) a cube well of length a and (2) a rectangular solid well with square cross-section of linear dimension b and of length c? (b) How does the ground state energy change from that of the cube with length a if (i) b = a and c = 4a? (The cube is stretched out.) Repeat for (ii) b = a and c = 0.5a. (The cube is squished). (c) For the cube and the two rectangular solids in (b), find the confinement energy (in eV) of the ground state for an electron if a = 2 nm. Compare them and explain the differences. (d) Show how the answers to (a) would change if the (effective) particle mass in each of the three dimensions needs to be treated as being different from each other (with masses mx, my and mz). (e) Repeat (c) for the case of (d) where the mass in the a (i.e. the x) direction is the free electron mass and those in the b and c (y and z) directions are one fifth of the free electron mass. Compare them and explain the differences.