Yangian与C.G.系数的升降算符求解及其Mathematica软件包

Yangian and the Calculation of C.G. Coeff icients with Shift Operators and Its Mathematica Package

利用 Yangian代数 Y(sl(2 ) )的一种实现 ,在量子力学原有升降算符的基础上 ,增加一个由Y(sl(2 ) )给出的算符 O± (j) ,得到了 C.G.(Clebsch- Gordan)系数的纯算符求法 ,这种求法具有更直观的物理意义 .并给出了根据这一理论编制的 Mathematica软件包 ,本软件包既能求出 C.G.系数的数值结果 ,又能求出其代数表达式 .

With a realization of th e Yangian algebra Y(sl(2)), on the basis of the shift operators in quantum mecha nics, by adding an operator O ±(j) from the Yangian associated with SL(2 ), we obtain a new method to calculate the Clebsch Gordan coefficients with onl y shift operators. Following this method, we also present a mathematica package. It can give not only the numerical results but also the formula results of the C.G. coefficients.