| Abstract: | By virtue of integration technique within ordered product of operators and Dirac’s representation theory we find a new general formula for normally ordering coordinate-momentum operator functions, that is (f(ghat {{Q}}+hhat {P})= :exp [textstyle {g^{2}+h^{2} over 4}textstyle {{partial ^{2}} over {partial (ghat {{Q}}+hhat {P})^{2}}}]f(ghat {{Q}}+hhat {P})):, where (hat {Q}) and (hat {P}) are the coordinate operator and momentum operator respectively, the symbol :: denotes normal ordering. Using this formula we can derive a series of new relations about Hermite polynomial and Laguerre polynomial, as well as some new differential relations. |
