Unitary and Hermit operators, and eigenvectors

Unitary and Hermit operators, and eigenvectors

Much of the mathematical apparatus of quantum mechanics appears in the classical mpsa44 description of a polarized sinusoidal electromagnetic wave. The Jones vector for a classical wave, for instance, is identical with the quantum mq250 polarization state vector for a photon. The right and left circular components of the Jones vector can be interpreted as probability amplitudes of spin states of the photon. mr4020 Energy conservation requires that the states be transformed with a unitary operation. This implies that infinitesimal transformations are transformed with a Hermit operator. These conclusions are a mrf151 natural consequence of the structure of Maxwell's equations for classical waves. Quantum mechanics enters the picture when observed quantities are measured and found to be discrete rather than continuous. The allowed observable mrf255 values are determined by the eigenvalues of the operators associated with the observable. In the case angular momentum, for instance, the allowed observable values are the eigenvalues of the spin operator.