[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.