Basic Distribution Functions in Classical Statistical Mechanics

BASIC DISTRIBUTION FUNCTIONS IN CLASSICAL STATISTICAL MECHANICS 

Derivation of the Boltzmann distribution function is based on statistical mechanical considerations and requires use of Stirling s approximation and Lagrange s method of undetermined multipliers to arrive at the basic equation, (N,/No) = (g/go)exp[-A Ae/]. The exponential term /3 defines the temperature scale of the Boltzmann function and can be shown to equal t/ksT. In classical mechanics, this distribution is defined by giving values for the coordinates and momenta for each particle in three-coordinate space and the lin- 

The approximate solution to the Schrodinger equation, defined by the effective Hamiltonian in Eq. (9-1), with either method described in the previous section, associates to every vector of molecule coordinates, R, together with the solvent-solvent interaction potential, an energy (R). From basic classical statistical mechanics an N-particle distribution function (PDF) n(R) is thus obtained  

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