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\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),  that fall o as N􀀀  M grows. But from a physical point of view it can be interpreted in this way: in the limit !0 !, the qubit causes a much weaker  boost on the system dynamics than that caused by the oscillator; therefore,  only transitions between states with the same N are energetically favoured.\end{comment}