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In Born-Oppenheimer approximation there is one step, when you divide your wavefunction into two pieces - first dependent on nuclei coordinates only and second dependent on electron coordinates only (the nuclei coordinates are treated as parameter here). The "global" wavefunction is a product of these two. Why "almost" independent movement of nuclei and electrons determine form of global wavefunction as product of electron and nuclei wavefunctions? What is mathematical proof of that?

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# I Born Oppenheimer problem

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