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Solving Hamiltonian with chain of charge centers?

  1. Apr 18, 2008 #1
    I was thinking of how to solve the single particle Hamiltonian
    [tex]H=...+\sum_i \frac{1}{\vec{r}-\vec{r}_i}[/tex]
    where [itex]\vec{r}_i=i\cdot\vec{a}[/itex]
    Transforming it into second quantization k-space I had terms like
    But it seems to me that for the method of trial wavefunctions any wavefunction [itex]\psi[/itex] gives zero matrix elements?!
    Is there anything wrong? How would I solve a potential from equally spaced chain of static point charges with a single electron moving?
    Last edited: Apr 18, 2008
  2. jcsd
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