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5. A particle of mass m, moves freelv inside an infinite potential well of length a, has the following initial wave function at t = U: A . HI 3 . 31m: 1 . 5m: '1' '4'" 0' Ta\" (7) + J53!" T) + E31" (T) where A is a real constant. a.} Find A so that '1' (x, D) is normalized. b.) If measurements of the energy are carried out, what are the values that will be found and what are the corresponding probabilities? Calculate the average energy. c.) Find the wave function 'P (x, t) at any later time t. d.) Determine the probability of finding the system at a time t in the state 11,5 (x, t) = 3 3m (52) 4:15.51) (1 a