The normalized wave function for a free particle is given by
⟨x∣ψ⟩=⎩⎨⎧a2cosaπx0∣x∣≤a/2∣x∣>a/2
Such a state might be created by putting the particle into the ground state of the potential energy box discussed in Section 6.9 and then instantaneously removing the potential. What is the probability that a measurement of the momentum yields a value between p and p+dp? Your final answer should not involve any complex numbers, since the probability of having momentum between p and p+dp is a real quantity. Simplify your answer as much as possible. Suggest a strategy for measuring this probability.