Thanks for the replies, now it actually starts to make sense.
Regarding your reply, blue_leaf77, I generally understand your approach but am wondering what exactly I have to write for ⟨x|p⟩. Would it be fine to just write it as the inner product
\begin{equation}
\langle x | p \rangle = \hat{X}...
Heads up, I only recently got into quantum mechanics and don't feel like I got a solid grasp on the material yet.
1. Homework Statement
Given is the wave function of a free particle in one dimension:
\begin{equation}
\psi(x,0) = \left( \frac{2}{\pi a^2} \right)^{1/4} e^{i k_0 x} e^{-x^2/a^2}...