Feynman's Principle Quantum amplitude is sum over all possible paths:

$$ \langle x_f|e^{-iHt/\hbar}|x_i\rangle = \int \mathcal{D}[x(t)] e^{iS[x]/\hbar} $$

Where $S[x]$ is the classical action:

$$ S[x] = \int_0^t L(x, \dot{x}, t') dt' $$

Key Idea Classical mechanics: One path (least action) Quantum mechanics: All paths …

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