# A free particle

A free particle has initial wavefunction:

$\Psi(x,0)=A\exp{-a|x|}$

where $A$ and $a$ are constants.

a) Normalize $\Psi(x,t)$.

b) Find $\Psi(x,t)$ and $|\Psi(x,t)|^2$.

c) Find the expectation value of the position $\langle x \rangle$, the square on the position $\langle x^2 \rangle$, the momentum $\langle p \rangle$ and the square on the momentum $\langle p^2 \rangle$.