Classical wave theory defines electromagnetic radiation as vector fields where energy density is proportional to the squared magnitude of amplitude superpositions in specific bases. Quantum mechanics reinterprets these classical amplitudes and phases such that their squares represent transition probabilities rather than continuous energy distributions, governed by discrete quanta (photons) characterized by Planck's constant times frequency. This duality establishes a bridge between linear differential equations describing field oscillations and probabilistic state collapses upon measurement in the context of quantum optics and wave mechanics.
Classical wave theory defines electromagnetic radiation as vector fields where energy density is proportional to the squared magnitude of amplitude superpositions in specific bases. Quantum mechanics…