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Re-expressing the Hamiltonian of a system using another basis
I have been given the Hamiltonian of system (particle in a ring),
H=∑0N[−V1(|gn⟩⟨gn+1|+|gn+1⟩⟨gn|)−V2(|gn⟩⟨gn+2|+|gn+2⟩⟨gn |)]It's expressed in the basis How can I re-express this in the basis, |hm⟩:hm(n)=e2πinm/N where, n=1,2,3... N-1 and show that it is diagonal? |
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