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- W2419013341 abstract "Studied is the problem of degeneracy of mechanical systems the configuration space of which is the three-dimensional sphere, the elliptic space, i.e., the quotient of that sphere modulo the antipodal identification, and finally, the three-dimensional pseudo-sphere, namely, the Lobatchevski space. In other words, discussed are systems on groups ${rm{SU}}(2)$, ${{rm{SO}}}(3,mathbb{R})$, and ${rm{SL}}(2,mathbb{R})$ or its quotient ${{rm{SO}}}(1,2)$. The main subject are completely degenerate Bertrand-like systems. We present the action-angle classical description, the corresponding quasi-classical analysis and the rigorous quantum formulas. It is interesting that both the classical action-angle formulas and the rigorous quantum mechanical energy levels are superpositions of the flat-space expression, with those describing free geodetic motion on groups." @default.
- W2419013341 created "2016-06-24" @default.
- W2419013341 creator A5055937876 @default.
- W2419013341 creator A5079182126 @default.
- W2419013341 date "2015-01-01" @default.
- W2419013341 modified "2023-10-18" @default.
- W2419013341 title "Bertrand Systems on Spaces of Constant Sectional Curvature. The Action-Angle Analysis. Classical, Quasi-Classical and Quantum Problems" @default.
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- W2419013341 doi "https://doi.org/10.7546/giq-16-2015-110-138" @default.
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