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## Homework Statement

At t=0 the particle is localized around [tex]x=x_0[/tex] that is: [tex]\langle x\rangle (0)=x_0[/tex], and the impulse is: [tex]\langle p\rangle (0)=\hbar k_0[/tex], we can describe the particle with the wave function:

[tex]\psi(x,0)=Ae^{-\frac{(x-x_0)^2}{2\sigma^2}+ik_0(x-x_0)}[/tex]

Now, my question is: If I have localized particle around [tex]x=x_0[/tex] but my expected value of impulse at t=0 is zero, that means that my particle is at rest. Is then the wave package given by this wave function?:

[tex]\psi(x,0)=Ae^{-\frac{(x-x_0)^2}{2\sigma^2}[/tex] ?