Manipulation of Phase-space Integrals

One way to reduce the problem slightly is to recognize that for many properties A, the position and momentum dependences of A are separable. In that case, Eq. (3.5) can be written as 

Since the Hamiltonian is also separable, the integrals in brackets on the r.h.s. of Eq. (3.31) may be simplified and we write 

Even with so large a simplification, however, the convergence of Eq. (3.32) for a realistically sized chemical system and a random selection of phase points is too slow to be useful. What is needed is a scheme to select important phase points in a biased fashion. 

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