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- W3102937461 abstract "We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We give the details of the Hamiltonian reduction of the 3D system to a 2D system with modified potential that is separable in elliptic coordinates. The potentials for which there is double-periodicity of the Schrodinger operator in the space of prolate spheroidal coordinates, including one for the H$_2^+$ molecular ion, are indicated. We study possible potentials that admit exact-solvability is as well as all models known to us with the (quasi)-exact-solvability property for the separation equations. We find deep connections between second-order superintegrable and conformally superintegrable systems and these tractable problems. In particular we derive a general 4-parameter expression for a model potential that is always integrable and is conformally superintegrable for some parameter choices." @default.
- W3102937461 created "2020-11-23" @default.
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- W3102937461 date "2014-04-25" @default.
- W3102937461 modified "2023-09-25" @default.
- W3102937461 title "Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability" @default.
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- W3102937461 doi "https://doi.org/10.1088/1751-8113/47/19/192002" @default.
- W3102937461 hasPublicationYear "2014" @default.
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