Feynman's path integral: the quantum amplitude for a particle to travel from A to B is the sum over ALL possible paths:
K(B,A) = ∫ 𝒟[x(t)] · exp(iS[x]/ℏ), where S[x] = ∫L dt is the classical action.
Each path contributes amplitude eiS/ℏ — unit magnitude, but varying phase. Paths far from the classical path have rapidly oscillating phases that cancel (stationary phase approximation).
As ℏ → 0, only the path of stationary action survives — this is the classical trajectory. Quantum mechanics is classical mechanics plus interference.