Hamilton-Jacobi treatment of a non-relativistic particle on a curved space

Details Hamilton-Jacobi treatment of a non-relativistic particle on a curved space Hamilton-Jacobi treatment of a non-relativistic particle on a curved space

2001-05-11

arxiv.org/abs/hep-th/0105109v1

J.Phys.A34:73-80,2001

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX

Scientific paper

10.1088/0305-4470/34/1/305

In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.

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