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Expectation value of momentum

  1. Nov 14, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle is in a infinite square poteltian well between x=0 and x=a. Find <p> of a particle whose wave function is [tex]\psi(x) = \sqrt{\frac{2}{a}}sin\frac{n \pi x}{a}[/tex] (the ground state).

    2. The attempt at a solution

    [tex]<p> = \frac{2 \hbar k}{\pi} \int^{a}_{0}sin^{2} \frac{\pi x}{a} dx = \frac{2 \hbar k }{\pi} \int^{\pi}_{0}sin^{2}u du = \hbar k = p[/tex]

    which certainly isn't the answer I wanted. The correct answer is 0. Where's my mistake?
  2. jcsd
  3. Nov 14, 2008 #2
    You get the wrong answer because you invented your own procedure to calculate <p>. Check your textbook for how to calculate the expectation value <A> of any operator A, in an arbitrary state psi.
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