Quantum Motion on 2D Surfaces of Spherical Topology |
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Authors: | X. Wang Y. P. Xiao T. G. Liu M. M. Lai J. Rao |
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Affiliation: | (1) School for Theoretical Physics and Department of Applied Physics, Hunan University, Changsha, 410082, China;(2) Department of Physics and Electronic Engineering, Hunan City University, Yiyang, 413049, China |
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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. PACS numbers: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization. |
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Keywords: | quantum mechanics canonical quantization |
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