# Ehrenfest's Theorem

1. Jul 28, 2005

### 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?

2. Jul 28, 2005

### Galileo

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).

3. Jul 28, 2005

### 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 ?

4. Jul 28, 2005

### robphy

Are you looking for Earnshaw's Theorem?

5. Jul 28, 2005

### DaTario

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

6. Jul 28, 2005

### yukcream

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

7. Jul 28, 2005

### Gokul43201

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