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When is classical mechanics valid for describing motion of atoms?

  1. Apr 12, 2013 #1
    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. jcsd
  3. Apr 12, 2013 #2

    Jano L.

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    Gold Member

    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...
     
  4. Apr 12, 2013 #3
    Last edited: Apr 12, 2013
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