Problem 1.8A particle confined in an infinite square well between x = 0 and x = L isprepared with wave functionde) = {1/VIif 0 < x < Lotherwise1. Does the particle have a well-defined energy?2. What is the probability to find the particle in the n'th bound state n(see Eq. 1.71) that has a well-defined energy En = (Tħn/L)²/2m?3. What is the average energy of the particle? Explain the the requirementthat physical wave functions don't have discontinuities, in view of youranswer.Problem 1.9Consider a particle in the n'th bound state ,n(x) (see Eq. 1.71) of an infinitesquare well between x = 0 and x = L.1. Use a symmetry argument to prove that (x) = L/2 where (x) is theaverage position computed from the results of many identical experi-ments.1.7. PROBLEMS35

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