Open AccessDifferential quotient rules of operator in composite function and its applications in quantum physics
Author(s) -
Sai Xu,
Xing-Lei Xu,
Hongqi Li,
JiSuo Wang
Publication year - 2014
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.63.240302
Subject(s) - operator (biology) , differential operator , semi elliptic operator , quotient , operator algebra , pure mathematics , ladder operator , wigner distribution function , displacement operator , momentum operator , operator theory , shift operator , physics , mathematical physics , algebra over a field , compact operator , quantum , quantum mechanics , mathematics , quasinormal operator , finite rank operator , computer science , repressor , biochemistry , transcription factor , gene , banach space , chemistry , programming language , extension (predicate logic)
Differential quotient rule of composite function operator and its applications in quantum physics, quantum statistics, operator ordering theory, matrix theory and control theory are given. The integration problem of Wigner operator and Weyl corresponding rules are studied. Two kinds of typical operator identity formulas are proved. The differential form of Wigner operator in ordered product of operators and new differential form of important functions are obtained. Finally, a Wigner operator with parameter for unifying regular order, Weyl sequencing and abnormal order is introduced.