The partition function and the sum or density of states are functions which are to statistical mechanics what the wave function is to quantum mechanics. Once they are known, all of the thermodynamic quantities of interest can be calculated. It is instructive to compare these two functions because they are closely related. Both provide a measure of the number of states in a system. The partition function is a quantity that is appropriate for thermal systems at a given temperature (canonical ensemble), whereas the sum and density of states are equivalent functions for systems at constant energy (microcanonical ensemble). In order to lay the groundwork for an understanding of these two functions as well as a number of other topics in the theory of unimolecular reactions, it is essential to review some basic ideas from classical and quantum statistical mechanics. As discussed in chapter 2, the classical Hamiltonian, H(p,q), is the total energy of the system expressed in terms of the momenta (p) and positions (q) of the atoms in the system.
Perturbation-Theory Rules for Computing the Self-Energy Operator in Quantum Statistical Mechanics