Polynomial Heisenberg algebras and higher order supersymmetry
David J. Fernandez C., Veronique Hussin
Abstract
It is shown that the higher order supersymmetric partners of the harmonic oscillator Hamiltonian provide the simplest non-trivial realizations of the polynomial Heisenberg algebras. A linearized version of the corresponding annihilation and creation operator leads to a Fock representation which is the same as for the harmonic oscillator Hamiltonian
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