Euler angle geometry, helicity basis vectors, and the Wigner D-function addition theorem
Euler angle geometry, helicity basis vectors, and the Wigner D-function addition theorem
复制标题
欧拉角几何、螺旋基向量和维格纳 D 函数加法定理
DOI：
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发表时间：
2003
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通讯作者：
J. D. Pendleton
中科院分区：
文献类型：
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作者：
J. D. Pendleton
欧拉角通常用于描述通过产生两个辅助系统和具有三个旋转的辅助系统相对于主系统旋转的辅助系统的取向。我们使用基向量来证明y约定欧拉角（用于量子力学）的辅助系统是与主笛卡尔系统相关联的圆柱和球形系统。然后，我们应用欧拉角几何得到一个改进的表达（和理解）的维格纳D-函数加法定理和相关的几何问题。我们引入螺旋度向量，并表示向量球谐函数的组合维格纳D-函数，以表明D-函数加法定理是隐含在旋转向量球谐函数的扩展。作为Wigner D函数的应用实例，我们得到了矢量球谐函数的加法定理，然后简化了一个描述激光照射下的非弹性光散射的并矢绿色函数（与Mie理论有关）。
Euler angles often are used to describe the orientation of a secondary system rotated relative to a primary system by generating two auxiliary systems and the secondary with three rotations. We use basis vectors to show that the auxiliary systems of the y-convention Euler angles (used in quantum mechanics) are the cylindrical and spherical systems associated with the primary Cartesian system. We then apply Euler angle geometry to obtain an improved expression (and understanding) of the Wigner D-function addition theorem and related geometrical issues. We introduce helicity vectors and express vector spherical harmonics as combinations of Wigner D-functions to show that the D-function addition theorem is implicit within expansions of rotated vector spherical harmonics. As example applications of the Wigner D-function, we obtain an addition theorem for vector spherical harmonics and then simplify a dyadic Green function (related to Mie theory) describing inelastic light scattering from a laser-irradiated sp...