2.4. A particle moves in an infinite cubic potential well described by: V(x1, x2) = {0 if 0 ≤ x1, x2 ≤ a otherwise 12= (a) Write down the exact energy and wave-function of the ground state. (2) (b) Write down the exact energy and wavefunction of the first excited states and specify their degeneracies. Now add the following perturbation to the infinite cubic well: H' = 18(x₁-x2) (c) Calculate the ground state energy to the first order correction. 2 (5) (d) Calculate the energy of the first order correction to the first excited degenerated state.

2.4. A particle moves in an infinite cubic potential well described by: V(x1, x2) = {0 if 0 ≤ x1, x2 ≤ a otherwise 12= (a) Write down the exact energy and wave-function of the ground state. (2) (b) Write down the exact energy and wavefunction of the first excited states and specify their degeneracies. Now add the following perturbation to the infinite cubic well: H' = 18(x₁-x2) (c) Calculate the ground state energy to the first order correction. 2 (5) (d) Calculate the energy of the first order correction to the first excited degenerated state.