Quantization (physics) attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in. One of the earliest attempts at a natural quantization was Weyl quantization, proposed by Hermann Weyl in 1927. Here, an attempt is made to associate a quantum-mechanical observable (a self-adjoint operator on a Hilbert space) with a real-valued function on classical phase space.
Heisenberg picture line above is the Heisenberg Hamiltonian "H"("t"), which may differ from the Schrödinger Hamiltonian. An important special case of the equation above is obtained if the Hamiltonian does not vary with time. Then the time-evolution operator can be written as Therefore, and, Here ∂"A"/∂"t" is the time derivative of the initial "A", not the "A"("t") operator defined. The last equation holds since commutes with . If the Hamiltonian does not vary with time, then the time-evolution operator can be written as where is the Hamiltonian and is the reduced Planck constant. Therefore, Thus and hence emerges the above Heisenberg equation