Semiclassical expansion theory in phase space

Year: 1995

Authors: Smerzi A.

Autors Affiliation: Department of Physics, University of Illinois at Urbana-Champaign 1110 West Green Street, Urbana, Illinois 61801-3080; Laboratorio Nazionale del Sud, Istituto Nazionale di Fisica Nucleare, via Andrea Doria, 95125 Catania, Italy

Abstract: We study the h perturbation expansion of the quantum Wigner equation. It leads to a unified formulation of semiclassical approximations based on the phase-space representation of quantum mechanics. We derive the O(h(2)) quantum corrections to the finite-temperature Bose and Thomas-Fermi phase-space distributions. Both reduce, in the high-temperature limit, to the known quantum corrections of the classical Gibbs-Boltzmann probability density. Within this approach, moreover, we obtain a very simple derivation of the extended Thomas-Fermi theory. Finally, the limits of applicability, the convergence problems, and the possibility of improving or defining new semiclassical approximations are discussed.

Journal/Review: PHYSICAL REVIEW A

Volume: 52 (6)      Pages from: 4365  to: 4370

KeyWords: Semi-classical Approximations; Nuclear Hamiltonians; Finite Temperature; Quantum-mechanics; Potentials; Dynamics; Equation
DOI: 10.1103/PhysRevA.52.4365

Citations: 14
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