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yukcream
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Can anyone tell me what is the Ehrenfest's Theorm in quantum mechanic, I don't understand how it can provide an example for correspondence principle?
Are you looking for Earnshaw's Theorem?DaTario said:Now I am a bit confused. What's the name of that theorem which forbids static electric and magnetic charges to produce stable equillibrium condition in 3D ?
Galileo said:Are you familiar with the equation of motion:
[tex]\frac{d}{dt}\langle Q \rangle = \frac{i}{\hbar}\langle [H,Q] \rangle + \langle \frac{\partial Q}{\partial t}\rangle[/tex]
where Q is an observable?
Try putting Q=p (momentum) and Q=r (position).
Ehrenfest's Theorem is a fundamental principle in quantum mechanics that relates the time evolution of quantum mechanical expectation values to the classical equations of motion. It was first proposed by Paul Ehrenfest in 1927.
Ehrenfest's Theorem states that the rate of change of the expectation value of a quantum mechanical observable is equal to the expectation value of the corresponding classical observable multiplied by a factor known as the quantum correction term. This allows us to connect the classical and quantum descriptions of a system.
Ehrenfest's Theorem is important because it allows us to understand the behavior of quantum mechanical systems in terms of classical mechanics, making it a powerful tool for analyzing and predicting the behavior of microscopic particles and systems.
Ehrenfest's Theorem has many practical applications in fields such as quantum chemistry, solid state physics, and particle physics. It is used to study the dynamics of atoms and molecules, the behavior of electrons in solids, and the interactions between subatomic particles.
While Ehrenfest's Theorem is a useful tool for understanding the behavior of quantum systems, it does have some limitations. It is only valid for systems that are in a stationary state, and it does not take into account quantum effects such as tunneling and entanglement. Additionally, it is only applicable to systems with a finite number of degrees of freedom.