# Allowed momentum values for a plane wave

Member advised to use the homework template for posts in the homework sections of PF.
Hi all,
This is from a past exam paper: At t=0 the state of a particle is described by the wavefunction

Code:
 $$\Psi (x,0) =A(iexp(ikx)+2exp(-ikx))$$

This is between positive and negative infinity - not in a potential well.

What values of momentum are allowed, and with what probability in each case?

Relevant Equations:
## \hat p = -i \hbar \frac{\partial}{\partial x} ##

My attempted solution:
Since there's only one k value present I was thinking there is one momentum value: ##p = \hbar k## with 100% chance of measuring this. And the fact that the uncertainty in position is infinite means that its momentum is sharp. But if this is the case, then why isn't it an eigenfunction of momentum?

Cheers

blue_leaf77
Homework Helper
Momentum is a vector operator - the sign matters.

• alec_grunn
Ok so that means 20% chance of +p and 80% chance of -p?

blue_leaf77