This article is cited in 5 papers

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

A. V. Shchepetilov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider the quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces. Using the group isometries, we obtain systems of ordinary differential equations for the energy levels. We prove that the Hamiltonian is self-adjoint for several interaction potentials. For the sphere, a number of energy series are evaluated for bodies with equal masses.

Received: 05.06.1998

DOI: 10.4213/tmf697

 English version: Theoretical and Mathematical Physics, 1999, 118:2, 197–208

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