Eur. Phys. J. D 57, 117-121 (2010)
https://doi.org/10.1140/epjd/e2010-00006-y

Quantum mechanics in phase space: first order comparison between the Wigner and the Fermi function

¹ CNISM, CNR-INFM, and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
³ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy

Corresponding author: giuliano.benenti@uninsubria.it

Received: 17 October 2009
Revised: 18 December 2009
Published online: 19 January 2010

Abstract

The Fermi g_F(x,p) function provides a phase space description of quantum mechanics conceptually different from that based on the the Wigner function W(x,p). In this paper, we show that for a peaked wave packet the g_F(x,p)=0 curve approximately corresponds to a phase space contour level of the Wigner function and provides a satisfactory description of the wave packet's size and shape. Our results show that the Fermi function is an interesting tool to investigate quantum fluctuations in the semiclassical regime.