# Solving Hamiltonian with chain of charge centers?

1. Apr 18, 2008

### Gerenuk

I was thinking of how to solve the single particle Hamiltonian
$$H=...+\sum_i \frac{1}{\vec{r}-\vec{r}_i}$$
where $\vec{r}_i=i\cdot\vec{a}$
Transforming it into second quantization k-space I had terms like
$$H=...+\sum_G...c^\dag_{k+G}c_k$$
But it seems to me that for the method of trial wavefunctions any wavefunction $\psi$ gives zero matrix elements?!
$$<\psi|c^\dag_{k+G}c_k|\psi>=<c_{k+G}\psi|c_k\psi>=0$$
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