The transformation (2.47) makes the implementation of the calculation quite sophisticated. Instead one can construct an approximate wave function in the same spirit as it will be done in the subsequent sections, i.e. by using the exact solution for the two particle scattering problem (1.60).
Using the solution (1.80) we propose
The advantage of this wave function is that it is solution of a two-body problem, so the interaction energy is always constant, which is much easier to sample numerically. The force and local energy can be easily obtained from hard-sphere wave function. The difference is that is a variational parameter here.
The drift force contribution (2.39) is given by
(2.49) |
The local energy (2.40) is
(2.50) |