By D.R. Bates and Benjamin Bederson (Eds.)
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The frequencies of the radiation given by classical mechanics are those harmonics present in the Fourier development of the position vector r ( t ) (Landau and Lifshitz, 1971), Eq. (49). The action variables are quantized according to the Bohr-Sommerfeld rule, but to preserve symmetry we write I = (n + n’)h/2 (53) The classical frequencies of emitted radiation are then wc(n, n’) = s * o(1) (54) where the fundamental frequency is a function of the action variables I and where s=n-n’ (55) We use the index c to denote classical quantities and the index q to denote the corresponding quantal variables.
DENSITY-OF-STATES CORRESPONDENCE PRINCIPLE It is generally accepted that macroscopic systems obey the laws of classical mechanics; but the transition from the quantum mechanics of atoms to the classical mechanics of macroscopic systems is more subtle than is 16 I . Percival and D . Richards commonly supposed. This transition is important for the application of classical mechanics to highly excited atoms. For example, the hydrogen atoms of interstellar space which emit the radio-recombination lines are as large as bacteria, but their spectrum is discrete and thus observed to be quantized.
1958)calculated several hundred trajectories on an Illiac machine; this was still not enough to provide adequate statistics for a reaction rate. The first true Monte Carlo calculation for a reaction was that of Blais and Bunker (1962). The method has been used extensively for atom-molecule collisions as reviewed by Bunker 46 I . C . Percival and D . Richards (1964, 1971), but the problems and techniques are somewhat different for collisions between charged particles and atoms due to the long range and attractive singularities of the Coulomb interaction.