# 3 molecules with a single excitation

1. Jan 15, 2014

### Bizarre123

I have 2 molecules and a single excitation (which can be on either molecule), i.e. I have the states: (using bra-ket notation)

$\left| E_{1} G\right\rangle$ and $\left| G E_{2}\right\rangle$

where $E_{1}$ is the excitation on molecule 1 and $G$ is the ground state. I'm happy that I can rewrite these states as:

$\frac{\left(\left| E_{1} G\right\rangle + \left| G E_{2}\right\rangle\right)}{√2}$

and

$\frac{\left(\left| E_{1} G\right\rangle - \left| G E_{2}\right\rangle\right)}{√2}$.

But what is the equivalent if I have 3 molecules and a single excitation? i.e. I now start with the states $\left| E_{1} G G\right\rangle$, $\left| G E_{2} G\right\rangle$ and $\left| G G E_{3} \right\rangle$, and want to rewrite them?

I think one of the new states should be $\frac{\left(\left| E_{1} G G\right\rangle + \left| G E_{2} G\right\rangle + \left| G G E_{3} \right\rangle \right)}{√3}$, but I'm not sure about the others?

Any help would be really appreciated- thanks!!