Ehrenfest theorem and Heisenberg quantum mechanics

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Discussion Overview

The discussion centers on the differences between the Ehrenfest theorem and the Heisenberg representation of quantum mechanics, exploring their relationship and whether one can be considered a consequence of the other. The scope includes theoretical aspects of quantum mechanics.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants describe the Ehrenfest theorem as providing equations of motion for the mean values of observables such as position and momentum.
  • Others explain that the Heisenberg picture shifts time dependence to operators rather than state vectors, offering equations of motion for operators instead of their mean values.
  • One participant questions whether the Ehrenfest theorem is a consequence of the Heisenberg equations of motion or if they can be considered distinct.
  • Another participant asserts that the Ehrenfest theorem can be derived without the Heisenberg picture, but acknowledges that using the Heisenberg picture makes the derivation trivial.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the Ehrenfest theorem and the Heisenberg picture, with some suggesting a connection while others maintain that they can be independent. The discussion remains unresolved regarding the nature of their relationship.

Contextual Notes

There are limitations regarding the assumptions made about the derivations and the definitions of the terms used, which may affect the clarity of the relationship between the two concepts.

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which 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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