非线性代数,阶梯算符与氢原子(英文)

Nonlinear Alagbra,Ladder Operators and the Hydrogen Atom

本文发现氢原于的哈密顿算符、角动量算符和阶梯算符自然生成了一个非线性李代数,根据非线性李代数理论,我们得到了氢原子的六个通用阶梯算符,它们不依赖于被作用状态的量子数。

In this paper,we find a new nonlinear Lie algebra which is generated naturally by the Hamilton operator,the angular momentum operator and the ladder operator for the hydrogen atom. According to the theory of the nonlinear Lie algebra,we obtained six universal ladder operators for the hydrogenatom,which are independent of the quantum numbers.