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A particle of mass m is con?ned in a one-dimensional in?nite well: V (x) = 0, if 0 ≤ x ≤ a; V (x) = ∞, if x < 0 or x > a. Its normalized wave function is ψ(x) = sqrt(8/5a)[1 + cos(πx/a)]sin(πx/a) inside the well. (a) Rewrite the wave function in terms of the normalized eigenfunctions: ψ = Σn Anψn. And determine the coe?cients An. (b) What values can the measured energy of the system possibly be? (c) What is the average energy of the system after many measurements?

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