In physics, the Heisenberg picture or Heisenberg representation[1] is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory.
It stands in contrast to the Schrödinger picture in which the operators are constant and the states evolve in time. The two pictures only differ by a basis change with respect to time-dependency, which corresponds to the difference between active and passive transformations. The Heisenberg picture is the formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal.
It further serves to define a third, hybrid, picture, the interaction picture.
^"Heisenberg representation". Encyclopedia of Mathematics. Retrieved 3 September 2013.
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In physics, the Heisenbergpicture or Heisenberg representation is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which...
is an intermediate representation between the Schrödinger picture and the Heisenbergpicture. Whereas in the other two pictures either the state vector...
^{*}} , which describes the action of Φ {\displaystyle \Phi } in the Heisenbergpicture: The spaces of operators L(HA) and L(HB) are Hilbert spaces with the...
Schrödinger picture, the Heisenbergpicture is often preferred in a relativistic context, that is, for quantum field theory. Compare with Dirac picture.: 65 ...
Werner Karl Heisenberg (pronounced [ˈvɛʁnɐ kaʁl ˈhaɪzn̩bɛʁk] ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers...
most apparent in the Heisenbergpicture of quantum mechanics, where it amounts to just the expectation value of the Heisenberg equation of motion. It...
quantum system. The two most important ones are the Heisenbergpicture and the Schrödinger picture. These differ only by a basis change with respect to...
to solving quantum dynamics is equivalent to the Schrödinger picture or Heisenbergpicture, it allows more easily for the inclusion of incoherent processes...
In mathematics, the Heisenberg group H {\displaystyle H} , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form ( 1...
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a...
A\mid \psi (t)\rangle } and that the time-dependent Heisenberg operators satisfy Heisenbergpicture (general) d d t A ( t ) = i ℏ [ H , A ( t ) ] + ∂ A...
\\-l_{1}&-l_{2}&-2l_{3}&-2\lambda \\\end{pmatrix}}.\end{aligned}}} In the Heisenbergpicture of quantum mechanics, an observable A without explicit time t dependence...
particularly relevant in quantum mechanics where the Schrödinger picture and Heisenbergpicture are (mostly)[clarification needed] equivalent descriptions of...
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous...
Schrödinger picture, even though this equation seems at first look to emulate the Heisenberg equation of motion in the Heisenbergpicture, with a crucial...
γ 0 γ j {\textstyle \alpha _{j}=\gamma _{0}\gamma _{j}} . In the Heisenbergpicture, the time dependence of an arbitrary observable Q obeys the equation...
This describes the channel in the Schrödinger picture. Taking adjoint maps in the Heisenbergpicture, the success condition becomes ⟨ Φ ( ρ ⊗ ω ) | I...
remain manifest. For example, the similarity between the Heisenberg equation in the Heisenbergpicture of quantum mechanics and the Hamilton equation in classical...
relativity. Although the earlier formulations, like the Schrödinger picture and Heisenbergpicture were originally formulated in a non-relativistic background...
the Schrödinger picture |Ψ(t)⟩ changes with time according to the Schrödinger equation while O is constant. In the Heisenbergpicture it is the other...
eigenstate of the annihilation operator in the Heisenbergpicture. It is easy to see that, in the Schrödinger picture, the same eigenvalue α ( t ) = e − i ω...
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