Open AccessAn integral-transformation corresponding to quantum mechanical fundamental commutative relation and its application in deriving Wigner function
Author(s) -
Zu-feng Liang,
Hong-Yi Fan
Publication year - 2015
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.64.050301
Subject(s) - wigner distribution function , transformation (genetics) , operator (biology) , kernel (algebra) , commutative property , quantum , mathematical physics , physics , pure mathematics , momentum (technical analysis) , function (biology) , quantum mechanics , momentum operator , mathematics , ladder operator , compact operator , computer science , evolutionary biology , programming language , extension (predicate logic) , repressor , chemistry , biochemistry , transcription factor , finance , economics , gene , biology
In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1/exp[2i(q-Q)(p-P)], here denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules(P-Q ordering, Q-P ordering and Weyl ordering). We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained.