论文标题
惯性张量的Bra-Ket表示
Bra-Ket Representation of the Inertia Tensor
论文作者
论文摘要
我们采用Dirac的烤面包符号来定义独立于基础或坐标系的惯性张量算子。仅根据几何形状确定椭圆板的主轴和相应的主值。通过使用一般的对称张量操作员，我们开发了一种对角化方法，该方法在确定特征向量时方便而直观。我们证明，Bra-Ket方法大大简化了惯性张量的计算，其中$ n $维椭圆形的示例。对经典力学中的惯性张量计算惯性张量的剥削应为本科生提供解决抽象量子力学问题所需的强大背景。
We employ Dirac's bra-ket notation to define the inertia tensor operator that is independent of the choice of bases or coordinate system. The principal axes and the corresponding principal values for the elliptic plate are determined only based on the geometry. By making use of a general symmetric tensor operator, we develop a method of diagonalization that is convenient and intuitive in determining the eigenvector. We demonstrate that the bra-ket approach greatly simplifies the computation of the inertia tensor with an example of an $N$-dimensional ellipsoid. The exploitation of the bra-ket notation to compute the inertia tensor in classical mechanics should provide undergraduate students with a strong background necessary to deal with abstract quantum mechanical problems.
