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-   -   Re-expressing the Hamiltonian of a system using another basis (https://www.askmehelpdesk.com/showthread.php?t=827680)

  • Sep 18, 2016, 01:56 PM
    danulagod
    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
    ⟨m|gn⟩=δmn

    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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