A particle of mass m is in the ground state of the infinite square well (Equation 2.22). Suddenly the well expands to twice its original size—the right wall moving from a to 2a—leaving the wave function (momentarily) undisturbed. The energy of the particle is now measured.
(a) What is the most probable result? What is the probability of getting that result?
(b) What is the *next* most probable result, and what is its probability? Suppose your measurement returned this value; what would you conclude about conservation of energy?
(c) What is the *expectation value* of the energy? *Hint:* If you find yourself confronted with an infinite series, try another method.