1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Electron group veloicty

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data
    A one-dimensional material has an applied time varying e-field as shown below:

    [tex]
    \epsilon(t)=\left\{\begin{array}{cc}A_1,&0\le t \le 2
    \\0,& 2\le t \le 4
    \\-A_1,& 4\le t \le 6
    \end{array}\right
    [/tex]

    The band structure of the material is [itex]E=\hbar\nu\|k\|[/itex], where [itex]\nu[/itex] is a constant with units of velocity. What is the electron gorup velocity as a function of time from 0 to 6?

    2. Relevant equations
    [tex]
    v=\frac{d\omega}{dk}=\frac{dE}{dp}
    [/tex]

    3. The attempt at a solution
    [tex]
    v_g=\frac{1}{\hbar}\frac{dE}{dk}
    [/tex]

    I'm not sure on how to include the e-field into this equation. Any suggestions?
     
  2. jcsd
  3. Nov 23, 2008 #2

    olgranpappy

    User Avatar
    Homework Helper

    Probably you just want to account for the fact that k depends on time via
    [tex]
    \frac{d\bold{k}}{dt}=-e\bold{E}(t)\;,
    [/tex]
    where
    [tex]
    \bold{E}(t)
    [/tex]
    is the electric field and [itex]-e[/itex] is the charge of the electron.
     
  4. Nov 24, 2008 #3
    Now I'm having trouble with the math part:
    [tex]
    dE=\hbar \nu dk
    [/tex]

    [tex]
    dk=-e\epsilon(t)dt
    [/tex]

    [tex]
    v_g=\frac{1}{\hbar}\frac{dE}{dk}=\frac{\nu dk}{-e\epsilon(t)dt}
    [/tex]

    where [itex]\epsilon[/itex] is the e-field. This doesn't really look right?
     
  5. Nov 25, 2008 #4

    olgranpappy

    User Avatar
    Homework Helper

    mmm... if you just forget about the electric field for a second and just look at
    [tex]
    E=\hbar v |k|\;,
    [/tex]
    what is the group velocity?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Electron group veloicty
  1. Galilean group (Replies: 9)

  2. Group Velocity (Replies: 1)

  3. Group Representation (Replies: 15)

Loading...