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\end{equation}  where $\alpha_{stnm}=\omega_0(\gamma_{st}-\gamma_{nm})$. Therefore, one can easily see that for $s=n$ and $t=m$ the matrix element becomes $=\delta_{MN}$ (since $D(0)=\id$).  As \textit{Rebolini} done in his thesis work \cite{ARebolini} I perform the \textit{adiabatic approximation} that consist in discarding the far-from diagonal matrix elements, i.e. for $M\neqN$.  \begin{comment} Adiabatic approximation consists in discarding the far-from diagonal matrix  elements (NM for N 6= M). This approximation can be legitimized  mathematically by inspecting the structure of Laguerre polynomials (2.2.3),