Coherent state and normal ordering method for transiting Hermite polynomials to Laguerre polynomials  

作　　者：FAN HongYi ZHOU Jun 

机构地区：[1]Department of Material Science and Engineering,University of Science and Technology of China,Hefei 230026,China [2]Department of Material and Chemical Engineering,West Anhui University,Lu'an 237012,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第4期605-608,共4页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10874174);the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070358009)

摘　　要：By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials. We also derive the new reciprocal relation of Laguerre polynomials ∑n=0 （-1）n （n^l）Ln （x） = x^l/n, n-O and its application in deriving the sum rule of the Wingner function of Fock states is demonstrated. Some new expansion identities about the operator Laguerre polynomial are also derived. This opens a new route of deriving mathematical polynomials formulas by virtute of the quantum mechanical representations and operator ordering technique.By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials.We also derive the new reciprocal relation of Laguerre polynomials n=0(1) n l n L n(x) = x l l!,and its application in deriving the sum rule of the Wingner function of Fock states is demonstrated.Some new expansion identities about the operator Laguerre polynomial are also derived.This opens a new route of deriving mathematical polynomials formulas by virtute of the quantum mechanical representations and operator ordering technique.

关 键 词：coherent state Hermite polynomial Laguerre polynomial normal ordering 

分 类 号：O174.41[理学—数学] O431.2[理学—基础数学]