d维各向同性谐振子的因式分解方法及广义Laguerre多项式
Factorization Method for d-Dimensional Isotropic Harmonic Oscillator and the Generalized Laguerre Polynomials
摘要：
将Infeld和Hull的因式分解方法应用于$d$维各向同性谐振子的径向薛定谔方程，定义了各种阶梯算符.径向能量本征态表示的广义拉盖尔多项式和它们的性质示出遵循从表达式涉及的阶梯运营商。用与谐振子相同的方法，我们也得到了Morse振子的束缚能本征态。
英文摘要：
The factorization method of Infeld and Hull is applied to the radial Schrödinger equation for $d$-dimensional isotropic harmonic oscillator and various ladder operators are defined. The radial energy eigenstates are expressed in terms of the generalized Laguerre polynomials and their properties are shown to follow from the expressions involving the ladder operators. In the same way as the harmonic oscillator we also obtain the bound energy eigenstates of the Morse oscillator.
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