Deriving uniform semiclassical approximations for one-dimensional fermionic systems
Raphael F. Ribeiro, Kieron Burke
A complete derivation is provided of the uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of non-perturbative quantum effects, including tunneling and quantum oscillations, via an infinite resummation of the Poisson summation formula. We explore the analytic behavior, physical meaning, and the relationship between the semiclassical uniform approximations for the fermionic kinetic energy and particle densities.
The Journal of Chemical Physics•May 16, 2018•13 citations