Abstract: By using the Runge-Lenz vector and angular momentum, three kinds of raising and lowering operators(Δ(l)=±l, Δ(m)=0, ±1)conserving the energy(Δ(n)=0)are constructed. It is demonstrated that these operators are equivalent to the angular momentum raising and lowering operators(Δ(l)=±1)derived from the factorization of the radial Schrodinger equation.

Key words: factorization, raising and lowering operators, Runge-Lenz vector, closeness of classical orbit

摘要： 利用三维氢原子的Runge-Lenz矢量和角动量构造出了保证能量不变(Δn=0)的三类升降算子(Δl=±1,Δm=0,±1)，证明它们与径向Schrodinger方程的因式分解所导出的角动量升降算子A±(l)等价。

关键词: 因式分解, 升降算子, Runge-Lenz矢量, 经典轨道的闭合性