# 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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