223
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Superintegrable Systems in Darboux spaces

      Preprint
      , , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Staeckel multiplier transformations). We present tables of the results.

          Related collections

          Most cited references8

          • Record: found
          • Abstract: not found
          • Article: not found

          On higher symmetries in quantum mechanics

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Coupling-Constant Metamorphosis and Duality between Integrable Hamiltonian Systems

              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              Completeness of superintegrability in two-dimensional constant curvature spaces

              We classify the Hamiltonians \(H=p_x^2+p_y^2+V(x,y)\) of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians \(H=J_1^2+J_2^2+J_3^2+V(x,y,z)\) on the complex 2-sphere where \(x^2+y^2+z^2=1\). This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.
                Bookmark

                Author and article information

                Journal
                18 July 2003
                Article
                10.1063/1.1619580
                math-ph/0307039
                cd1cd11a-5657-4090-9cd0-c4c0a7643e2c
                History
                Custom metadata
                37K05 70H20
                IMA 1929
                J. Math. Phys. 44 (2003) 5811-5848
                math-ph math.MP

                Comments

                Comment on this article