Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces

DOI10.1007/BF02557312zbMath0966.81013MaRDI QIDQ1568008

Alexey V. Shchepetilov

Publication date: 26 June 2000

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

zbMATH Keywords

group isometriesHamiltonian is self-adjoint

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (2)-body potential quantum scattering theory (81U05)

Related Items (3)

Two-body problem on two-point homogeneous spaces, invariant differential operators and the mass center concept. ⋮ Two-body problem on spaces of constant curvature. I: Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system ⋮ Two-body problem on spaces of constant curvature. II: Spectral properties of the Hamiltonian

Uses Software

• Maple

Cites Work

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• Kepler's problem in constant curvature spaces
• Some quantum mechanical problems in Lobachevsky space
• Path integral treatment of the hydrogen atom in a curved space of constant curvature
• Constraints, reduction, and quantization
• Dynamical symmetries in a spherical geometry. I
• Dynamical symmetries in a spherical geometry. II
• Reduction of the two-body problem with central interaction on simply connected spaces of constant sectional curvature
• Reduction, quantization, and nonunimodular groups
• On a New Treatment of Some Eigenvalue Problems

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