Abstract
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.
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PACS numbers: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization.
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Wang, X., Xiao, Y.P., Liu, T.G. et al. Quantum Motion on 2D Surfaces of Spherical Topology. Int J Theor Phys 45, 2464–2470 (2006). https://doi.org/10.1007/s10773-006-9214-0
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DOI: https://doi.org/10.1007/s10773-006-9214-0