Equations of Electron Dispersion in an E Field

[goorioles747]

Homework Statement

Given the dispersion equation of an electron in an electric field:

Homework Equations

a) calculate the velocity of the electron if k = π/a

b) If the electric field E is applied in the -x direction, derive the time
dependence of k for an electron initially at k = π/a and position x = 0.

c) Derive the time dependence of the electron velocity, v(t), and the
time dependence of the electron position, x(t).

The Attempt at a Solution

for a, do they mean the group velocity which is a function of 1/hbar * dE/dk?

 

[nickjer]

My guess is yes. It makes little sense to just calculate the phase velocity for a single frequency.

 

[goorioles747]

And would you set the E = .5mv²? Or can you not because of the uncertainty principle?

 

[nickjer]

The dispersion isn't quadratic so there is no classical kinetic energy term. I am guessing that you are giving the dispersion for an electron in a crystal. Since you are lacking in details.