- #1
ognik
- 643
- 2
Homework Statement
The text states:
"Let us consider a wave packet whose Fourier inverse ##\phi (\vec{k})## is appreciably different from zero only in a limited range ##\Delta \vec{k}## near the mean wave vector ##\hbar \vec{\bar{k}} ##. In coordinate space, the wave packet ##\psi(\vec{r}, t)## must move approximately like a classical free particle with mean momentum ##\hbar \vec{\bar{k}}##. To see this behavior we expand ##\omega (\vec{k})## about ##\vec{\bar{k}}##:
## \omega (\vec{k}) = \omega(\vec{\bar{k}}) + (\vec{k} - \vec{\bar{k}}) \cdot (\vec{\nabla_k} \omega)_{k= \vec{\bar{k}}} + ...##
##=\bar{\omega} + (\vec{k} - \vec{\bar{k}})\cdot \vec{\nabla_{\bar{k}}} \bar{\omega} +... ## with obvious abbreviations"
I'm afraid not much of the above is obvious to me ... have searched all over but no progress ... please help me understand -
What expansion are they using and where do they get it from?
What are the abbreviations mentioned?