In Feynman's lecture (I am forgetting the volume number) while explaining the least action principle he mentions that the system actually follows all possible configuration paths. $\exp(iS/\hbar)$ superposes constructively for the values of action $S$ for which it is stationary with respect to the variations of the path. This argument is comprehensible but what is the actual quantum mechanical basis of this argument?
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3For a concise (if somewhat dated) exposition of this argument, see e.g. Feynman, R. P., "Principles of least action in quantum mechanics", PhD Thesis, Princeton University (1942). – Emilio Pisanty Feb 25 '21 at 19:16
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Possible duplicate: https://physics.stackexchange.com/q/8663/2451 – Qmechanic Feb 25 '21 at 20:49