Ehrenfest theorem and Heisenberg quantum mechanics

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SUMMARY

The Ehrenfest theorem provides the equations of motion for the mean values of observables such as position and momentum in quantum mechanics. In contrast, the Heisenberg picture shifts the time dependence to operators rather than state vectors, eliminating the need for Schrödinger's equations and substituting them with the Heisenberg equations of motion. The Ehrenfest theorem can be derived independently of the Heisenberg picture, although using the Heisenberg framework simplifies the derivation process. This discussion clarifies the relationship between these two fundamental concepts in quantum mechanics.

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  • Understanding of quantum mechanics fundamentals
  • Familiarity with the Ehrenfest theorem
  • Knowledge of the Heisenberg picture of quantum mechanics
  • Basic grasp of operators and observables in quantum systems
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  • Study the derivation of the Ehrenfest theorem in detail
  • Explore the Heisenberg equations of motion
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Students and professionals in physics, particularly those specializing in quantum mechanics, as well as educators seeking to clarify the distinctions and connections between the Ehrenfest theorem and the Heisenberg picture.

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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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