scholarly journals Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature

2006 ◽  
Author(s):  
Francisco José Herranz
Keyword(s):  
Constant Curvature ◽  
Three Dimensional ◽  
Spaces Of Constant Curvature

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

scholarly journals HYDROGEN ATOM AS AN EIGENVALUE PROBLEM IN 3-D SPACES OF CONSTANT CURVATURE AND MINIMAL LENGTH

1999 ◽  
Vol 14 (35) ◽  
pp. 2463-2469 ◽  
Author(s):  
L. M. NIETO ◽  
M. SANTANDER ◽  
H. C. ROSU
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Constant Curvature ◽  
Three Dimensional ◽  
Minimal Length ◽  
Positive Zero ◽  
Spaces Of Constant Curvature ◽  
Curvature Effects ◽  
Negative Constant ◽  
Space Curvature

An old result of Stevenson [Phys. Rev.59, 842 (1941)] concerning the Kepler–Coulomb quantum problem on the three-dimensional (3-D) hypersphere is considered from the perspective of the radial Schrödinger equations on 3-D spaces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wave function for the hydrogen atom case. Finally, we make a comparison between the "space curvature" effects and minimal length effects for the hydrogen spectrum.

Simplexes in spaces of constant curvature

1991 ◽  
Vol 38 (1) ◽  
Author(s):  
B.V. Dekster ◽  
J.B. Wilker
Keyword(s):  
Constant Curvature ◽  
Spaces Of Constant Curvature
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