Ehrenfest's Theorem

yukcream

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?

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Galileo

Homework Helper
Are you familiar with the equation of motion:

$$\frac{d}{dt}\langle Q \rangle = \frac{i}{\hbar}\langle [H,Q] \rangle + \langle \frac{\partial Q}{\partial t}\rangle$$

where Q is an observable?
Try putting Q=p (momentum) and Q=r (position).

DaTario

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 ?

robphy

Homework Helper
Gold Member
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 ?
Are you looking for Earnshaw's Theorem?

DaTario

hehehehe....thank you a lot... I am getting old, my son...

yukcream

Galileo said:
Are you familiar with the equation of motion:

$$\frac{d}{dt}\langle Q \rangle = \frac{i}{\hbar}\langle [H,Q] \rangle + \langle \frac{\partial Q}{\partial t}\rangle$$

where Q is an observable?
Try putting Q=p (momentum) and Q=r (position).

It is just the result of the theorem! Any mathematical divide inside?

Gokul43201

Staff Emeritus
Gold Member
Yes, the mathematics of showing the correspondence principle at work comes from doing what Galileo suggested and arriving at the classical equations of motion.

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