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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 different energies are orthogonal.

(c) find out the ratio of the probabilities that various energy states are occupied if a measurement 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 mean energy < ˆH > compatible with this measurement?

(e) What is the corresponding wave function?

(f) For the system in this state of lowest mean energy, what is the probability of finding the system in its lowest energy state?

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