The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach. II
- Departamento de Fisica Teorica and IUMA, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain)
- Departamento de Fisica Teorica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid (Spain)
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, S{sub {kappa}}{sup 3} ({kappa} > 0) and H{sub k}{sup 3} ({kappa} < 0), to the standard spherical waves in E{sup 3}. The curvature {kappa} is considered as a parameter and for any {kappa} we show how the radial Schroedinger equation can be transformed into a {kappa}-dependent Gauss hypergeometric equation that can be considered as a {kappa}-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 {kappa}-dependent and {kappa}-independent), and are explicitly obtained.
- OSTI ID:
- 22093754
- Journal Information:
- Journal of Mathematical Physics, Vol. 53, Issue 10; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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