Ehrenfest theorem and Heisenberg quantum mechanics

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The Ehrenfest theorem describes the equations of motion for the mean values of observables such as position and momentum. In contrast, the Heisenberg picture shifts time dependence to operators rather than state vectors, providing equations of motion for the operators themselves. The Heisenberg framework eliminates the need for Schrödinger's equations, replacing them with Heisenberg's equations of motion. While the Ehrenfest theorem can be derived independently of the Heisenberg picture, using it simplifies the derivation significantly. Both concepts are distinct yet interconnected in quantum mechanics.
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Wich are the differences between the theorem of ehrenfest and the Heisenberg's rappresentation of quantum mechanics?
 
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The Ehrenfest theorem states what are the equation of motion for the mean value of observables like Position and Momentum

The Heisenberg picture moves the time dependence of the system to operators instead of state vector. So it provides the equation of motions for the operators not for their mean value over a state. In Heisenberg picture there is no more need of a Schroedinger equations (for the state vector) because it is now substituted by the Heisenberg equation of motions (for the operators).
 
ruleva1983 said:
The Ehrenfest theorem states what are the equation of motion for the mean value of observables like Position and Momentum

The Heisenberg picture moves the time dependence of the system to operators instead of state vector. So it provides the equation of motions for the operators not for their mean value over a state. In Heisenberg picture there is no more need of a Schroedinger equations (for the state vector) because it is now substituted by the Heisenberg equation of motions (for the operators).

yes i know, but my question is to be intended in differrent manner. is the theorem of ehrenfest a consequence of the equation of motion of Heisenberg or they can be differents?
 
Ehrenfest theorem can be derived even without using the Heisenberg picture, but if that picture is used then the derivation is trivial. Is it an answer to your question?
 
Demystifier said:
Ehrenfest theorem can be derived even without using the Heisenberg picture, but if that picture is used then the derivation is trivial. Is it an answer to your question?
yes it is
 

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