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Additional resources for Advances in Atomic and Molecular Physics 11
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.
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