Mathematical Details
In the Heisenberg picture of quantum mechanics the state vector, does not change with time, and an observable A satisfies
where H is the Hamiltonian and is the commutator of A and H. In some sense, the Heisenberg picture is more natural and fundamental than the Schrödinger picture, especially for relativistic theories. Lorentz invariance is manifest in the Heisenberg picture.
This approach has a similarity to classical physics: by replacing the commutator above by the Poisson bracket, the Heisenberg equation becomes an equation in Hamiltonian mechanics.
By the Stone-von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent.
Read more about this topic: Heisenberg Picture
Famous quotes containing the words mathematical and/or details:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“Patience is a most necessary qualification for business; many a man would rather you heard his story than granted his request. One must seem to hear the unreasonable demands of the petulant, unmoved, and the tedious details of the dull, untired. That is the least price that a man must pay for a high station.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)