A bead of mass m slides without friction on a straight wire of length a between two rigid walls. (a) What are the energy levels of the system?

A bead of mass m slides without friction on a straight wire of length a between two rigid walls. (a)What are the energy levels of the system? (b) Show explicitly that the wave function corresponding to differentenergies are orthogonal. (c) Calculate the ratio of the probabilities that various energy states are occupied if ameasurement indicates that the beads is exactly at the middle of the wire.A later measurement shows that the bead is not on the right half of the wire. (d) What is the lowest meanenergy < ˆH > compatible with this measurement? (e) What is the corresponding wave function? (f) For thesystem in this state of lowest mean energy, what is the probability of finding the system in its lowest energy state?