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Classical Integrable and Separable Hamiltonian Systems

  • Maciej Błaszak
Chapter

Abstract

In this chapter we introduce the concept of classical integrability of Hamiltonian systems and then develop the separability theory of such systems based on the notion of separation relations introduced by Sklyanin. Separation relations are the most fundamental objects of modern separability theory as well as allow for classification of all separable systems. We concentrate our attention on the subclass of separable systems for which all constants of motion are quadratic in momenta. This class of systems is most interesting from the physical point of view on both classical and quantum level.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maciej Błaszak
    • 1
  1. 1.Division of Mathematical PhysicsFaculty of Physics UAMPoznańPoland

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