Communications in Mathematical Physics

, Volume 83, Issue 3, pp 355–386 | Cite as

Classical and quantum-mechanical systems of Toda lattice type. I

  • Roe Goodman
  • Nolan R. Wallach


The structure of the commutant of Laplace operators in the enveloping and “Poisson algebra” of certain generalized “ax +b” groups leads (in this article) to a determination of classical and quantum mechanical first integrals to generalized periodic and non-periodic Toda lattices. Certain new Hamiltonian systems of Toda lattice type are also shown to fit in this framework. Finite dimensional Lax forms for the (periodic) Toda lattices are given generalizing results of Flaschke.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Hamiltonian System 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Roe Goodman
    • 1
  • Nolan R. Wallach
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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