Equations of Electron Dispersion in an E Field

AI Thread Summary
The discussion revolves around calculating the velocity of an electron in an electric field using its dispersion equation. The group velocity is suggested as the relevant measure, derived from the relation 1/hbar * dE/dk, rather than the phase velocity. There is uncertainty regarding the application of classical kinetic energy equations due to the non-quadratic nature of the dispersion relation. The context implies that the dispersion pertains to electrons in a crystal, highlighting the need for clarity in the problem statement. Overall, the complexities of quantum mechanics and the uncertainty principle are central to the calculations being discussed.
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Homework Statement



Given the dispersion equation of an electron in an electric field:
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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?
 
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My guess is yes. It makes little sense to just calculate the phase velocity for a single frequency.
 
And would you set the E = .5mv2? Or can you not because of the uncertainty principle?
 
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.
 
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