2. (5 points) Classical vs quantum infinite square well. (a) Consider a classical system of particle of mass m with value of momentum p in infinite square well. What is the classical probability distribution pa(a) for this particle ? (b) Take a quantum energy eigenfunction for infinite square well and sketch the corresponding probability density for some large n (You can use Mathematica and see what the plot looks like for say n = 20). (c) Perform the average of the quantum probability density over the period of os- cillation. Does it agree with classical result? (d) In the limit of large n, take the difference between the energy levels n + 1 and n and compute the corresponding frequency, i.c. v = (Ent1 - En)/h. Rewrite it using the wavelength of the quantum wave inside the well. (e) Compare it with the classical frequency, using de Broglie formula