Two-body problem on spaces of constant curvature. II: Spectral properties of the Hamiltonian

DOI10.1007/BF02551003zbMath1115.37333MaRDI QIDQ5941984

I. È. Stepanova, Alexey V. Shchepetilov

Publication date: 28 August 2001

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Two-body problems (70F05) Many-body theory; quantum Hall effect (81V70) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Applications of PDEs on manifolds (58J90) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (5)

Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2 ⋮ Classical dynamics of fullerenes ⋮ Two-body problem on two-point homogeneous spaces, invariant differential operators and the mass center concept. ⋮ Unnamed Item ⋮ Motion of test bodies with internal degrees of freedom in non-Euclidean spaces

Cites Work

• Unnamed Item
• Chaos in classical and quantum mechanics
• Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces
• A classification of the unitary irreducible representations of \(SO_ 0 (N,1)\)
• Dynamical symmetries in a spherical geometry. I
• Superintegrability on the two-dimensional hyperboloid. II
• Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions
• Two-body problem on spaces of constant curvature. I: Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system

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