三维各向同性谐振子和二元Krawtchouk多项式的基间展开
Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials
摘要：
利用标准Krawtchouk多项式和对偶Hahn多项式得到了一般二元Krawtchouk多项式的显式表达式。二元Krawtchouk多项式作为SO（3）在三维各向同性谐振子能量本征空间上的酉可约表示的矩阵元出现，并通过将这些表示分解为它们的不可约分量得到了显式表达式.分解需要在跨越不可约SO（3）表示的球基中扩展笛卡尔基态。重叠系数由su（1，1）李代数的Clebsch-Gordan问题得到。
英文摘要：
An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible representations of SO(3) on the energy eigenspaces of the 3-dimensional isotropic harmonic oscillator and the explicit formula is obtained from the decomposition of these representations into their irreducible components. The decomposition entails expanding the Cartesian basis states in the spherical bases that span irreducible SO(3) representations. The overlap coefficients are obtained from the Clebsch-Gordan problem for the su(1,1) Lie algebra.
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