Creation and annihilation operators, symmetry and supersymmetry of the 3D isotropic harmonic oscillator

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We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method.
Original languageAmerican English
Pages (from-to)4849-4856
Number of pages4363
JournalJournal of Physics A: Mathematical and General
StatePublished - 2 May 2003


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