Physics – Mathematical Physics
Scientific paper
2012-01-26
Journal of Mathematical Physics {\bf 52}, 072104 (2011)
Physics
Mathematical Physics
Scientific paper
10.1063/1.3610674
The quantum free particle on the sphere $S_\kappa^2$ ($\kappa>0$) and on the hyperbolic plane $H_\kappa^2$ ($\kappa<0$) is studied using a formalism that considers the curvature $\k$ as a parameter. The first part is mainly concerned with the analysis of some geometric formalisms appropriate for the description of the dynamics on the spaces ($S_\kappa^2$, $\IR^2$, $H_\kappa^2$) and with the the transition from the classical $\kappa$-dependent system to the quantum one using the quantization of the Noether momenta. The Schr\"odinger separability and the quantum superintegrability are also discussed. The second part is devoted to the resolution of the $\kappa$-dependent Schr\"odinger equation. First the characterization of the $\kappa$-dependent `curved' plane waves is analyzed and then the specific properties of the spherical case are studied with great detail. It is proved that if $\kappa>0$ then a discrete spectrum is obtained. The wavefunctions, that are related with a $\kappa$-dependent family of orthogonal polynomials, are explicitly obtained.
Cariñena José F.
Rañada Manuel F.
Santander Mariano
No associations
LandOfFree
The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-446044