Open AccessMatrix Elements of Arbitrary Exponential Quadratic Operator in Multi－ Dimensional Phase Space
Author(s) -
Xu Xiu-wei,
Jun Zhao,
Ren Ting-Qi
Publication year - 2000
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.49.17
Subject(s) - eigenfunction , exponential function , quadratic equation , operator (biology) , hamiltonian (control theory) , phase space , matrix (chemical analysis) , quartic function , energy operator , physics , mathematical analysis , mathematics , eigenvalues and eigenvectors , quantum mechanics , energy (signal processing) , pure mathematics , mathematical optimization , biochemistry , geometry , chemistry , materials science , repressor , transcription factor , composite material , gene
Utilizing the normal and antinomal product representative of exponential quadrat ic operator in multidimensional phase space we give the exact expressions of matrix element for arbitrary exponential quadratic operator. Thus we derive the partition function and wave function of the system of quadratic Hamiltonian with out the knowledge of energy spectrum and eigenfunctions.