How Can You Calculate the Expectation Value of Momentum in Quantum Mechanics?

[kasse]

Homework Statement

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

2. The attempt at a solution

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

which certainly isn't the answer I wanted. The correct answer is 0. Where's my mistake?

 

[borgwal]

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.