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• W2051499949 abstract "The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E &lt; 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results." @default.
• W2051499949 created "2016-06-24" @default.
• W2051499949 creator A5064149452 @default.
• W2051499949 creator A5088127739 @default.
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• W2051499949 date "2014-10-01" @default.
• W2051499949 modified "2023-10-01" @default.
• W2051499949 title "Classical and quantum dynamics in an inverse square potential" @default.
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• W2051499949 doi "https://doi.org/10.1063/1.4899083" @default.
• W2051499949 hasPublicationYear "2014" @default.
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