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:
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)
“Then he told the news media
the strange details of his death
and they hammered him up in the marketplace
and sold him and sold him and sold him.
My death the same.”
—Anne Sexton (1928–1974)