Polynomial Heisenberg algebras and higher order supersymmetry
classification
🪐 quant-ph
hep-thmath-phmath.MP
keywords
algebrashamiltonianharmonicheisenberghigherorderoscillatorpolynomial
read the original 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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