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Symmetries of the Self-Similar Potentials | V.Spiridonov
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1 Mar 1993 | Subject: | hep-th | Abstract: | 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. | Source: | arXiv, hep-th/9303004 | Services: | Forum | Review | PDF | Favorites |
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