Heisenberg equation

The Heisenberg equation is an equation describing the evolution of a quantum observable Hamiltonian system obtained by Werner Heisenberg in 1925. This equation has the form:

{d \over dt}A={i \over \hbar }[H,A]+{\frac {\partial A}{\partial t}},

{\ displaystyle {d \ over dt} A = {i \ over \ hbar} [H, A] + {\ frac {\ partial A} {\ partial t}},}

{\ displaystyle {d \ over dt} A = {i \ over \ hbar} [H, A] + {\ frac {\ partial A} {\ partial t}},}

Where $\ A$ ${\ displaystyle \ A}$ $\ A$ - quantum observable, which can explicitly depend on time, $\ H$ ${\ displaystyle \ H}$ $\ H$ Is the Hamilton operator , and the brackets denote the switch . In the case of open , dissipative and non-Hamiltonian quantum systems, the Lindblad equation is used for the quantum observable. If we take the coordinates and momentum operators as observables, then we obtain the quantum analogues of the classical Hamilton equations .

This equation, in particular, implies the Ehrenfest equation , if the average observables are taken as the quantum observable. In classical mechanics , the Hamilton equations are an analog of the reduced Heisenberg equation .

Literature

Lunev F. A., Sveshnikov K. A., Sveshnikov N. A., Timofeevskaya O. D., Khrustalev O. A. Introduction to quantum theory. Quantum mechanics. - M .: Publishing House of Moscow State University, 1985. - p. 63.
Medvedev B.V. The beginnings of theoretical physics. Mechanics. Field theory. Elements of quantum mechanics . - M .: Science, 1977. - P. 464.
Messia A. Quantum mechanics. In 2 volumes / Ed. L.D. Faddeev. Translation from French V.T. Khozyainova .. - M .: Science, 1978. - T. 1. - p. 307.
Timofeevskaya, OD, Khrustalev, OA Lectures on quantum mechanics. - Moscow-Izhevsk: RHD, 2007. - p. 12-13.
Fermi E. Quantum mechanics (lecture notes) . - M .: Mir, 1965. - p. 171-173.

Heisenberg equation

See also

Literature

More articles: