Symmetries of the Self-Similar Potentials

Details Symmetries of the Self-Similar Potentials Symmetries of the Self-Similar Potentials

1993-03-01

arxiv.org/abs/hep-th/9303004v1

Commun.Theor.Phys. 2:149-163,1993

Physics

High Energy Physics

High Energy Physics - Theory

9 pp., Latex (to appear in Comm.Theor.Phys.)

Scientific paper

An application of the particular type of nonlinear operator algebras to spectral problems is outlined. These algebras are associated with a set of one-dimensional self-similar potentials, arising due to the q-periodic closure f_{j+N}(x)=qf_j(qx), k_{j+N}=q^2 k_j of a chain of coupled Riccati equations (dressing chain). Such closure describes q-deformation of the finite-gap and related potentials. The N=1 case corresponds to the q-oscillator spectrum generating algebra. At N=2 one gets a q-conformal quantum mechanics, and N=3 set of equations describes a deformation of the Painleve IV transcendent.

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