%0 Journal Article
%T Higher-order supersymmetric quantum mechanics
%A David J Fernandez C
%A Nicolas Fernandez-Garcia
%J Mathematics
%D 2005
%I arXiv
%R 10.1063/1.1853203
%X We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the higher-order case. The second order technique is addressed directly, and through this approach unexpected possibilities for designing spectra are uncovered. The formalism is applied to the harmonic oscillator: the corresponding H-SUSY partner Hamiltonians are ruled by polynomial Heisenberg algebras which allow a straight construction of the coherent states.
%U http://arxiv.org/abs/quant-ph/0502098v2