Is energy quantized in classical physics

Quantization

Quantization, Quantization, the transition from classical physical theories to the corresponding quantum theories. There is no unambiguous quantization procedure; the principle of correspondence, according to which in the Limes H

0 the classical theory should follow (if it exists at all) and general requirements, such as that of the positivity of energy, do not completely determine the quantization. In all quantization methods, certain commutation relations are established for the operators of quantum theory or - more generally - the algebraic properties of these operators.

In quantum mechanics, depending on the representation, one encounters two equivalent methods, Schrödinger's method and Heisenberg's or canonical method. In the first case one obtains the Schrödinger wave mechanics, in the second case the Heisenberg matrix mechanics (quantum mechanics). At the Schrödinger's method quantization consists in the statistical interpretation of the wave function to be determined as the solution of the time-dependent Schrödinger equation. At the Heisenbergschen or canonical procedure physical quantities such as position, momentum and energy are not considered to be ordinary functions (c-number functions), but as operator-valued functions (q-number functions), which meet certain interchangeability rules (commutator).

The transition from classical mechanics to quantum mechanics can generally be established through the following correspondences: The physical quantity F.(q, p), as a function of the canonically conjugated variable q and p understood, go to the observable

as a function of the Hermitian operators

and

above, and the Poisson bracket



goes over to the commutator