单粒子本征波函数的对称性与势形状

以单核子在原子核三轴椭球形变势中运动的本征值方程为例,说明核形状决定了核势的形状,核势形状的对称性决定了在其势中运动的单粒子本征态的对称性.当核势形状的对称性随形变参量的改变而改变时,对应单粒子本征态对称性的改变,可以用量子力学中的表象变换来表现,也可以用波函数的表象变换来认识.此问题虽然来自于原子核结构理论,但其思想对于在原子、分子、团族粒子等量子体系中处于平均场中运动的独立粒子问题具有普遍意义.

Symmetry of eigen-functions for a single particle and the shape of the potential

It is shown,by an example of a single nucleon moving in a triaxial deformed potential,that the symmetry of the eigen-functions of the particle is determined by the form of the potential,and the potential is in turn dependent on the shape of the nucleus which produces it.When the symmetry of the potential varies with the deformation parameter,the change of the symmetry for the eigen-function can be expressed through the representation transformation of the quantum mechanics calculation or by the representation transformation of the eigen-function.Although the problem comes from nuclear structure theory,the idea of this work has the common significance for an independent particle moving in a mean field such as in quantum systems of atoms,molecules and clusters.