A note on the wigner distribution function |
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| Affiliation: | 1. Advanced Materials Engineering and Modelling Group, Wroclaw University of Science and Technology, Wroclaw, Poland;2. Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Tsinghua University, Beijing, China;3. Laboratory of NMR Spectroscopy, Department of Chemistry, University of Warsaw, Warsaw, Poland;4. Department of Theoretical Chemistry and Computer Science Group, Faculty of Mathematics, Physics and Chemistry, University of Silesia, Katowice, Poland;1. Shanghai Institute of Traumatology and Orthopaedics, Shanghai Key Laboratory for Prevention and Treatment of Bone and Joint Diseases, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, P.R. China;2. Department of Nanotechnology Engineering, University of Waterloo, Waterloo, ON, Canada;1. ECOBIOMAR, Instituto de Investigaciones Marinas (CSIC), Eduardo Cabello 6, 36208 Vigo, Spain;2. Comercial Hospitalaria Grupo 3, Arroncal 9, Vial C, Nave 4C, Porto do Molle, 36350 Nigrán, Spain;3. Larpro Engineering, S.L. Príncipe 57, 2°D, 36202 Vigo, Spain |
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| Abstract: | We rigorously prove that in general it is impossible to obtain a nonnegative phase-space distribution function through averaging a Wigner distribution function (WDF) over the finite phase-space cells. Moreover, we introduce a classification of WDFs according to the possibility of performing such an averaging procedure. Some examples of WDFs are also briefly discussed. |
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