In Volume II Chapter 19 of his Lectures on Physics, Feynman discusses the principle of least action and its role in quantum mechanics. He says the following on page 19-9:(adsbygoogle = window.adsbygoogle || []).push({});

"The complete quantum mechanics (for the nonrelativistic case and neglecting electron spin) works as follows: The probabilty that a particle starting at point 1 at the time [tex]t_{1}[/tex] will arrive at point 2 at the time [tex]t_{1}[/tex] is the square of a probability amplitude. For every x(t) we could have-for every possible imaginary trajectory-we have to calculate an amplitude. Then we add them all together. What do we take for the amplitude for each path? Our action integral tells us what the amplitude for a single path ought to be. The amplitude is proportional to some constant times [tex]e^{iS/\hbar}[/tex], where S is the action for that path."

Why does Feynman make the qualification "for the nonrelativistic case and neglecting electron spin"? Doesn't the same principle apply even relativistically in calculating the probability amplitude for a path?

Any help would be greatly appreciated.

Thank You in Advance.

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# The Principle of Least Action in Quantum Physics

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