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3 molecules with a single excitation

  1. Jan 15, 2014 #1
    I have 2 molecules and a single excitation (which can be on either molecule), i.e. I have the states: (using bra-ket notation)

    [itex]\left| E_{1} G\right\rangle[/itex] and [itex]\left| G E_{2}\right\rangle[/itex]

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

    [itex]\frac{\left(\left| E_{1} G\right\rangle + \left| G E_{2}\right\rangle\right)}{√2}[/itex]

    and

    [itex]\frac{\left(\left| E_{1} G\right\rangle - \left| G E_{2}\right\rangle\right)}{√2}[/itex].

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

    I think one of the new states should be [itex]\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}[/itex], but I'm not sure about the others?

    Any help would be really appreciated- thanks!!
     
  2. jcsd
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