Finding Momentum and Uncertainty in Quantum Mechanics Problem 1.17

[asdf60]

Problem 1.17 in griffiths gives, at time t = 0, the state psi =A(a^2-x^2) for -a to a, and 0 otherwise. It asks then to find the expected value of momentum p at 0 and also the uncertainty in p. How do I do this? The only way momentum is defined is md<x>/dt, and since the state is only for time t, there seems to be no way to do this.

I know that if i take Fourier transform the wave function i'll get the expected momentum, but I don't think that's what the problem wants me to do. Is there a simpler way?

 

[asdf60]

never mind, I'm an idiot.

 

[quantumdude]

Glad we could help.

 

[Reshma]

Glad we could help.