1. Limited time only! Sign up for a free 30min personal 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!

Dispersion relation

  1. May 5, 2005 #1
    Hi, please could someone explain the term dispersion relation to me, particularly for the case of a free electron?

    Thanks

    Jayse
     
  2. jcsd
  3. May 5, 2005 #2

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In wave theory, a dispersion relation is the relation between the wave number and the angular frequency: [tex]k(\omega)[/tex]. There are also integral relations in S matrix theory that are an integral representation of this. For a free electron, the dispersion relation you refer to must be relating p to E since each is just [tex]\hbar[/tex] times k and [tex]\omega[/tex]. In SR, this is [tex]p=\sqrt{E^2-m^2}[/tex]. It could be used in the electron wave function, so that the group velocity would be
    dE/dp=p/E (all with c=1).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook