Abstract
When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2μ) ∑ pi2 with hermitian form of Cartesian momentum pi (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/fi)pifipi where the functions fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this article, the explicit forms of the dummy functions fi for quantum motion on some 2D surfaces of revolution of spherical topology are given.
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