- #1

Bill Foster

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- 0

## Homework Statement

Consider two fermion states:

[tex]|n_1 n_2\rangle = a_{n_1}^\dagger a_{n_2}^\dagger|0\rangle[/tex]

and

[tex]|n_1 n_3\rangle = a_{n_1}^\dagger a_{n_3}^\dagger|0\rangle[/tex]

where [tex]a_n^\dagger[/tex] denotes the fermion creation operator in the single-particle state [tex]u_n\left(\vec{r},s\right)[/tex]. Evaluate the matrix elements of the one-body operator [tex]\hat{O}=\sum_{nn'}\langle n|O|n'\rangle a_n^\dagger a_{n'}^\dagger[/tex] between these two states.

## The Attempt at a Solution

Not sure if I should start out like this:

[tex]\langle 0| a_{n_1}^\dagger a_{n_2}^\dagger \sum_{nn'} \langle n|O|n'\rangle a_n^\dagger a_{n'}^\dagger a_{n_1}^\dagger a_{n_3}^\dagger |0\rangle[/tex]

of if I should start out like this:

[tex]\langle n_1 n_2 | \sum_{nn'} \langle n|O|n'\rangle a_n^\dagger a_{n'}^\dagger|n_1 n_3\rangle[/tex]