2. Consider a particle in a 2-dimensional infinite square well given by: V(x) = {0 for 0≤x≤a and 0 ≤ y ≤a otherwise (a) What are the energy eigenvalue and the eigenket (eigenfunction) for the non- degenerate level? (b) What are the energy eigenvalue and the eigenket (eigenfunction) for the first excited state level? (c) What are the energy eigenvalue and the eigenket (eigenfunction) for the second excited state level? (d) The particle is now subjected to the perturbation given by: V(x) = {Cxy for 0≤x≤a and 0 ≤ y ≤ a 0 otherwise Where C is a constant. (i) Determine the first-order energy correction (shift) (ii) Find the wavefunction of the first excited level

2. Consider a particle in a 2-dimensional infinite square well given by: V(x) = {0 for 0≤x≤a and 0 ≤ y ≤a otherwise (a) What are the energy eigenvalue and the eigenket (eigenfunction) for the non- degenerate level? (b) What are the energy eigenvalue and the eigenket (eigenfunction) for the first excited state level? (c) What are the energy eigenvalue and the eigenket (eigenfunction) for the second excited state level? (d) The particle is now subjected to the perturbation given by: V(x) = {Cxy for 0≤x≤a and 0 ≤ y ≤ a 0 otherwise Where C is a constant. (i) Determine the first-order energy correction (shift) (ii) Find the wavefunction of the first excited level