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Two molecules

(Reading assigment: revision of statistical density operator).

We assume the unperturbed state (no interaction) of the two molecules described by a (quantum statistical) density operator

$\displaystyle \hat{\rho} = \sum_{kk'}P_{kk'} \vert kk'\rangle \langle kk'\vert,$     (2.17)

where the undashed indices refer to molecule 1 and the dashed ones to molecule 2. We call the unperturbed eigenvalues of \bgroup\color{col1}$ {\mathcal H}_0$\egroup
$\displaystyle E_{kk'} \equiv E_k + E_{k'}$     (2.18)

and define the effective interaction as
$\displaystyle V_{\rm eff}$ $\displaystyle \equiv$ $\displaystyle \sum_{kk'} p_{kk'} \langle kk'\vert T(E_{kk'}) \vert kk'\rangle$ (2.19)
  $\displaystyle =$ $\displaystyle \sum_{kk'} P_{kk'} \langle kk'\vert V \vert kk'\rangle +
\sum_{kk'} P_{kk'} \langle kk'\vert VG_0(E_{kk'}) V \vert kk'\rangle +...$  
  $\displaystyle \equiv$ $\displaystyle V_{\rm eff}^{(1)} + V_{\rm eff}^{(2)} + ...$ (2.20)

We write the interaction potential operator \bgroup\color{col1}$ V$\egroup
$\displaystyle V = \sum_i v_i \otimes v_i'$     (2.21)

as a sum over products of operators belonging to molecule 1 and molecule 2. We furthermore assume uncorrelated classical probabilities
$\displaystyle P_{kk'} = p_k p_{k'}.$     (2.22)


next up previous contents index
Next: First oder term: static Up: Effective Interaction between Molecules Previous: The -Matrix   Contents   Index
Tobias Brandes 2005-04-26