Classical Mechanical Treatment of Gas-Solid Collisions

While no one presently doubts that quantum mechanics forms the general theoretical framework for the discussion of molecular processes, the question of what is the most convenient computational algorithm for certain classes of problems is open. 

For problems involving heavy-particle dynamics and in situations where appreciable averaging is involved, classical or semiclassical methods [3.12,13] often prove acceptable. For these problems it is often the case that classical mechanics provides a poor picture of the elementary aspects of the process (e.g., specific transition probabilities) while at the same time it gives a rather good estimate of more-averaged quantities (e.g., energy transfer). 

We note in passing that by adopting a semiclassical viewpoint [3.13] it is often possible to extend an essentially classical framework to the point that it provides a quantitative treatment of the more elementary features of the collision dynamics. 

Before explicitly considering classical mechanical applications to gas-surface dynamics, it is useful to note the following general structure of the results. If the probability distribution function for some quantity, x, is known, P(x), and some function of x is formed, f(x), then the distribution function for f, g f)j is given by 

In the delta function f (without) with an argument denotes (a specified numerical value) the function s value at the point x. Since the delta function vanishes except at the roots of the equation 

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