Dispersion relation

  • Thread starter Jayse_83
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Hi, please could someone explain the term dispersion relation to me, particularly for the case of a free electron?

Thanks

Jayse
 

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Meir Achuz
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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).
 

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