Eur. Phys. J. Special Topics 227, 2171–2182 (2019)
https://doi.org/10.1140/epjst/e2018-800063-2

Regular Article

From von Neumann to Wigner and beyond

¹ Institute for Quantum Science and Engineering, Texas A&M University, Texas, USA
² Hunter College, City University of New York, New York, USA
³ Graduate Center, City University of New York, New York, USA
⁴ Baylor University, Waco, TX, USA
⁵ Princeton University, Princeton, NJ, USA

^a e-mail: j.s.ben-benjamin@tamu.edu

Received: 16 April 2018
Received in final form: 2 August 2018
Published online: 21 February 2019

Abstract

Historically, correspondence rules and quantum quasi-distributions were motivated by classical mechanics as a guide for obtaining quantum operators and quantum corrections to classical results. In this paper, we start with quantum mechanics and show how to derive the infinite number of quantum quasi-distributions and corresponding c-functions. An interesting aspect of our approach is that it shows how the c-numbers of position and momentum arise from the quantum operator.