论文标题
氢算子分解氢的方法
Cartesian operator factorization method for Hydrogen
论文作者
论文摘要
我们将施罗辛格的分解方法从常规分离到角度和径向坐标为基于笛卡尔的分解。这是这种方法所独有的，事实是，在依赖每个笛卡尔方向依赖坐标和动量的耦合运算符方面，哈密顿量被表示为对因素的总和。我们确定本征态和能量，坐标和动量空间中的波形，我们还说明了如何采用该技术来开发常规的汇合高几何方程方法。此处开发的方法可能会用于其他哈密顿量，这些方法可以表示为耦合的施罗辛格因素化的总和。
We generalize Schroedinger's factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach, is the fact that the Hamiltonian is represented as a sum over factorizations in terms of coupled operators that depend on the coordinates and momenta in each Cartesian direction. We determine the eigenstates and energies, the wavefunctions in both coordinate and momentum space, and we also illustrate how this technique can be employed to develop the conventional confluent hypergeometric equation approach. The methodology developed here could potentially be employed for other Hamiltonians that can be represented as the sum over coupled Schroedinger factorizations.
