Abstract
When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2m)∑ 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/(2m)∑ (1/fi)pifipi where the functions fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. The existence of non-trivial fi shows the universality of this constraint induced operator ordering in quantum kinetic energy operator for the constraint systems.
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