Quantum Motion on 2D Surfaces of Spherical Topology

When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2μ) ∑ p _i ² with hermitian form of Cartesian momentum p _i (i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2μ) ∑ (1/f _i )p _i f _i p _i where the functions f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this article, the explicit forms of the dummy functions f _i for quantum motion on some 2D surfaces of revolution of spherical topology are given. PACS numbers: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization.