I am given the following equation for the group velocity in one-dimension:

$$v_g = \frac{d\omega}{dk}.$$

In solid state physics one has $-\pi/a \leq k \leq \pi/a$ for a one-dimensional lattice with atoms where $a$ is the equilibrium distance between atoms. But my questions are: Is $k$ in the equation of the group velocity the absolute value of $k$ so rather $v_g = \frac{d\omega}{d|k|}$ and how can we generalize this to 3D for example?

  • $\begingroup$ In 3D, $v_g$ will be a vector quantity, just like $k$ $\endgroup$ – By Symmetry Jan 14 at 13:34
  • $\begingroup$ And what is $k$ in the 1D case? Is this the absolute value? $\endgroup$ – Dani Jan 14 at 13:37
  • $\begingroup$ no. In the 1D case $k$ is just $k$ $\endgroup$ – By Symmetry Jan 14 at 13:43

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.