[Q]Expression of Group velocity in QM

[good_phy]

Hi.

We already know Group velocity is $\frac{\partial w }{\partial k }$

But, liboff said Group velocity is $\frac{\partial w }{\partial k }|_{k_{max}}$ where $k_{max}$ is wave number which probability this value can be measured is higher than other wave number.

is it right? How can?

 

[jtbell]

In general, $\omega$ is a function of k, $\omega(k)$, so $d\omega / dk$ is another function of k. To get a particular velocity, you need to specify some value of k to evaluate $d\omega / dk$ at.