Abstract
When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2m)∑ 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/(2m)∑ (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. The existence of non-trivial f i shows the universality of this constraint induced operator ordering in quantum kinetic energy operator for the constraint systems.
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Liu, Q.H. Universality of Operator Ordering in Kinetic Energy Operator for Particles Moving on two Dimensional Surfaces. Int J Theor Phys 45, 2137–2142 (2006). https://doi.org/10.1007/s10773-006-9179-z
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DOI: https://doi.org/10.1007/s10773-006-9179-z