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- Ehrenfest_theorem abstract "The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist, relates the time derivative of the expectation value for a quantum mechanical operator to the expectation of the commutator of that operator with the Hamiltonian of the system, expectations which are connected to classical mechanics.It readswhere A is some QM operator and is its expectation value.Ehrenfest's theorem is most apparent in the Heisenberg picture of quantum mechanics, where it is just the expectation value of the Heisenberg equation of motion. It provides mathematical support to the correspondence principle.The reason is that Ehrenfest's theorem is closely related to Liouville's theorem of Hamiltonian mechanics, which involves the Poisson bracket instead of a commutator. Dirac's rule of thumb suggests that statements in quantum mechanics which contain a commutator correspond to statements in classical mechanics where the commutator is supplanted by a Poisson bracket multiplied by iħ. This makes the operator expectation values obey corresponding classical equations of motion, provided the Hamiltonian is at most quadratic in the coordinates and momenta. Otherwise, the evolution equations still may hold approximately, provided fluctuations are small.".
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- Ehrenfest_theorem subject Category:Quantum_mechanics.
- Ehrenfest_theorem subject Category:Theorems_in_quantum_physics.
- Ehrenfest_theorem comment "The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist, relates the time derivative of the expectation value for a quantum mechanical operator to the expectation of the commutator of that operator with the Hamiltonian of the system, expectations which are connected to classical mechanics.It readswhere A is some QM operator and is its expectation value.Ehrenfest's theorem is most apparent in the Heisenberg picture of quantum mechanics, where it is just the expectation value of the Heisenberg equation of motion. ".
- Ehrenfest_theorem label "Ehrenfest theorem".
- Ehrenfest_theorem label "Ehrenfest-Theorem".
- Ehrenfest_theorem label "Teorema de Ehrenfest".
- Ehrenfest_theorem label "Teorema de Ehrenfest".
- Ehrenfest_theorem label "Teorema di Ehrenfest".
- Ehrenfest_theorem label "Théorème d'Ehrenfest".
- Ehrenfest_theorem label "Twierdzenie Ehrenfesta".
- Ehrenfest_theorem label "Теорема Эренфеста".
- Ehrenfest_theorem label "エーレンフェストの定理".
- Ehrenfest_theorem label "埃倫費斯特定理".
- Ehrenfest_theorem sameAs Ehrenfestovy_teorémy.
- Ehrenfest_theorem sameAs Ehrenfest-Theorem.
- Ehrenfest_theorem sameAs Θεώρημα_του_Έρενφεστ.
- Ehrenfest_theorem sameAs Teorema_de_Ehrenfest.
- Ehrenfest_theorem sameAs Théorème_d'Ehrenfest.
- Ehrenfest_theorem sameAs Teorema_di_Ehrenfest.
- Ehrenfest_theorem sameAs エーレンフェストの定理.
- Ehrenfest_theorem sameAs 에렌페스트_정리.
- Ehrenfest_theorem sameAs Twierdzenie_Ehrenfesta.
- Ehrenfest_theorem sameAs Teorema_de_Ehrenfest.
- Ehrenfest_theorem sameAs m.07pv44.
- Ehrenfest_theorem sameAs Q908669.
- Ehrenfest_theorem sameAs Q908669.
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