"Interactions that look instantaneous are well suited to Schrödinger’s equation, which requires the potential between particles at equal times. It would be quite awkward to explicitly describe finite-velocity forces in the Schrödinger equation because the potential for one particle at a time t would depend on the positions of the others at the retarded times, and one would need the past histories of all the particles to propagate the system forward in time."
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Richard P. Feynman and James M. Cline:
https://en.wikiquote.org/wiki/Schr%C3%B6dinger_equation
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Schrödinger equation
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