The core principle is that quantum states and observables in photon polarization can be rigorously represented using Dirac notation (kets for vectors, bras for duals) where physical probabilities correspond to the squared modulus of inner products between state vectors. Formal definitions include Hermitian matrices representing measurable operators with real eigenvalues corresponding to experimental outcomes, complex conjugation defining bra-vectors and matrix adjoints, and normalization ensuring unit probability amplitudes for identical states within linear algebraic vector spaces over complex numbers. This formalism provides a deterministic mathematical framework that accurately predicts probabilistic experimental results in quantum mechanics, distinguishing itself from classical wave descriptions by encoding energy attenuation as the reduction of photon counts rather than field amplitude changes alone.
The core principle is that quantum states and observables in photon polarization can be rigorously represented using Dirac notation (kets for vectors, bras for duals) where physical probabilities cor…