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 (18901960)
“Working women today are trying to achieve in the work world what men have achieved all alongbut men have always had the help of a woman at home who took care of all the other details of living! Today the working woman is also that woman at home, and without support services in the workplace and a respect for the work women do within and outside the home, the attempt to do both is taking its tollon women, on men, and on our children.”
—Jeanne Elium (20th century)