When is classical mechanics valid for describing motion of atoms?

[Arham]

Hello. In Molecular Dynamics simulations, the Newton's equation of motion is used to calculate the time evolution of system. Once, I read in an introductory text that when the thermal de Broglie wavelength $$\Lambda=\frac{h}{\sqrt{2\pi mkT}}$$ is much smaller than the interparticle distance, using classical mechanics is justified and it can be used instead of quantum mechanics. Why? I mean I'd like to start from the Schrödinger equation or a theorem which is based on it (e.g. Ehrenfest's theorem) and using the above criterion obtain the Newton's equation of motion.

May you help me?

 

[Jano L.]

It is not easy to derive the Newton equations of motion from Schroedinger's equation alone, because the latter is usually though to be only a probabilistic description of the motion of the particles, while the Newton equations are direct description of trajectory. It is like with diffusion equation - you can't use it to derive trajectory of a Brownian particle.

The reason why the Newton equations are used is rather that they are simple and there are good reasons to think they are adequate - kinetic theory of gases...

 

[BacalhauGT]

http://en.wikipedia.org/wiki/Ehrenfest_theorem

hope this helps you

edit: "expectations which are connected to classical mechanics." you should read "General example"