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arXiv · 0808.2289

Factorization Method for d-Dimensional Isotropic Harmonic Oscillator and the Generalized Laguerre Polynomials

Metin Arık·Melek Baykal·Ahmet Baykal
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Abstract

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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Metin Arık, Melek Baykal, Ahmet Baykal. 2010-01-06. Factorization Method for d-Dimensional Isotropic Harmonic Oscillator and the Generalized Laguerre Polynomials. https://arxiv.org/abs/0808.2289

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