Calculate the spin wave dispersion relation for a ferromagnetic heisenberg model

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Homework Statement


Calculate the spin wave dispersion relation Ek for the ferromagnetic heisenberg model with jtot = 1/2
Assume a 1d square lattice and interactions of strength J between nearest neighbours and zero elsewhere

Homework Equations



H|k> = [E0 +2jtot[itex]\sum J(r)(1-Exp(ik.r) [/itex]] |k>


The Attempt at a Solution



Not really sure where to start :/

Homework Statement





Homework Equations





The Attempt at a Solution

 

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