Deformations and Nonlinear Systems
Deformations and Nonlinear Systems
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr��dinger equation are considered. The procedure is generalized to broader class of nonlinearities related to other types of deformations. The nonlinear noncanonical transforms used in the deformation procedure are shown to preserve in some cases the linear dynamical equations, for instance, for the harmonic oscillators. The nonlinear coherent states and some physical aspects of the deformations are reviewed.
23 pages,LATEX, to be published in Rend.Sem.Mat.Univ.Polit.Torino, volume 54 (1996), as Proceedings of Workshop on "Geometry and Plysics" Vietri Sept.29 1996, (S.Benenti, G.Marmo, A.Simoni, Eds.)
Quantum Physics, deformation, FOS: Physical sciences, Coherent states, wave equation, Schrödinger equation, nonlinear vibrations, Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics, Quantum Physics (quant-ph), PDEs in connection with quantum mechanics, harmonic oscillators
Quantum Physics, deformation, FOS: Physical sciences, Coherent states, wave equation, Schrödinger equation, nonlinear vibrations, Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics, Quantum Physics (quant-ph), PDEs in connection with quantum mechanics, harmonic oscillators
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