Abstract
An algebraic description of the class of 1D supersymmetric shape invariant potentials is investigated in terms of the shape-invariant-potential (SIP) deformed algebra, the generators of which act both on the dynamical variable and on the parameters of the potentials. The phase space geometry associated with SIP's is studied by means of a coherent state (SIP-CS) path integral and the ray metric of the SIP-CS manifold. The anharmonicity of SIP's results in a inhomogeneous phase space manifold with one Killing vector and with a modified symplectic Kähler structure, and it induces a non constant curvature into the generalized phase space. Analogous results from the phase space geometry of someq-deformed quantum algebras are briefly contrasted with those for the supersymmetric potentials. A star product operating between phase space symbols of operators is also suggested.
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Ellinas, D. Anharmonicity deformation and curvature in supersymmetric potentials. Czech J Phys 44, 1009–1018 (1994). https://doi.org/10.1007/BF01690453
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DOI: https://doi.org/10.1007/BF01690453