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• W3100960306 abstract "This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, Sκ3 (κ > 0) and Hk3 (κ < 0), to the standard spherical waves in E3. The curvature κ is considered as a parameter and for any κ we show how the radial Schrödinger equation can be transformed into a κ-dependent Gauss hypergeometric equation that can be considered as a κ-deformation of the (spherical) Bessel equation. The specific properties of the spherical waves in the spherical case are studied with great detail. These have a discrete spectrum and their wave functions, which are related with families of orthogonal polynomials (both κ-dependent and κ-independent), and are explicitly obtained." @default.
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• W3100960306 date "2012-10-01" @default.
• W3100960306 modified "2023-10-04" @default.
• W3100960306 title "The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach. II" @default.
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• W3100960306 doi "https://doi.org/10.1063/1.4757604" @default.
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