Ehrenfest's Theorem: Quantum Mechanics Explained

[yukcream]

Can anyone tell me what is the Ehrenfest's theorem in quantum mechanic, I don't understand how it can provide an example for correspondence principle?

 

[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).

 

[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]

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]

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]

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