Back to Search
Start Over
The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach. II.
- Source :
-
Journal of Mathematical Physics . Oct2012, Vol. 53 Issue 10, p102109-102109-19. 1p. - Publication Year :
- 2012
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 53
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 82963779
- Full Text :
- https://doi.org/10.1063/1.4757604