Uniform semiclassical approximations for many-particle 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.

Brian R. Landry

Raphael F. Ribeiro, Kieron Burke

A thorough account is given of the derivation of 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 effects via an infinite resummation of the Poisson summation formula.

Shimon Levit

Pierre Gaspard, Sudhir R Jain

Charles Jaffé

A new method for the quantization of classical Hamiltonian systems is presented. This method is based upon the correspondence between the Liouville formulation of classical mechanics and the Liouville–von Neumann formulation of quantum mechanics. It does not distinguish between integrable and nonintegrable systems, and consequently, is equally applicable to both types of systems. Further, it treats the indistinguishability of identical particles correctly, and thus, the semiclassical eigenstates have the correct symmetry properties. Application of the method is illustrated by a series of examples. The results are in excellent agreement with quantum mechanics and represent an improvement over results obtained using the uniform semiclassical approximation.