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Problem 3 Consider a particle with wave function localized between r = 0 and r = L, of the form 2 ( I, t ) otherwise. a) What is the probability of measuring the particle's position to be between r = L/3 and I == 21/3? (Remember ()|2 is the probability density function to observe the particle at z.) b) Show that this wave function does satisfy the time-dependent Schrodinger equation with V(z) = 0 between r =: 0 and r = L