Allowed momentum values for a plane wave

[alec_grunn]

Hi all,
This is from a past exam paper: At t=0 the state of a particle is described by the wavefunction

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

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?

Please help,
Cheers

 

[blue_leaf77]

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]

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

Yes.