Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states

Abstract

Using an iterative construction of the first-order intertwining technique, we find k-parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below E0 = ½. It is seen that the `natural' ladder operators for these systems give place to polynomial nonlinear algebras, and it is shown that these algebras can be linearized. The coherent states construction is performed in the nonlinear and linearized cases.