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I was just going through random lecture notes on Born-Oppenheimer approximation where I came across the following statement:

We first invoke the Born-Oppenheimer approximation by recognizing that, in a dynamical sense, there is a strong separation of time scales between the electronic and nuclear motion, since the electrons are lighter than the nuclei by three orders of magnitude.

My confusion is: what does separation of time scales actually mean ?

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Separation of time scales means that the characteristic times of movement (oscillation period, damping time, etc.) of the two systems are very different; this is also known as adiabatic approximation. If we take for simplicity that both nuclei and electrons perform oscillatory motion with periods $T_n$ and $T_e$, then $$T_e \ll T_n,$$ so that we can think of nuclei as static when solving the equations-of-motion for the electrons.

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