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

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

2008-08-17

arxiv.org/abs/0808.2289v2

Physics

Mathematical Physics

Improved presentation. Eqns. (29) and (31) corrected. References changed. 10 pages, 1 figure

Scientific paper

The factorization method of Infeld and Hull is applied to the radial Schr\"{o}dinger 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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