# When is classical mechanics valid for describing motion of atoms?

1. Apr 12, 2013

### 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 Schrodinger 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?

2. Apr 12, 2013

### 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...

3. Apr 12, 2013

### BacalhauGT

Last edited: Apr 12, 2013