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arXiv · 0910.0769

Constraint-induced mean curvature dependence of Cartesian momentum operators

Q. H. Liu·C. L. Tong·M. M. Lai
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Abstract

The Hermitian Cartesian quantum momentum operator $\mathbf{p}$ for an embedded surface $M$ in $R^{3}$ is proved to be a constant factor $-i\hbar $ times the mean curvature vector field $H\mathbf{n}$ added to the usual differential term. With use of this form of momentum operators, the operator-ordering ambiguity exists in the construction of the correct kinetic energy operator and three different operator-orderings lead to the same result. PACS: 03.65.-w Quantum mechanics, 04.60.Ds Canonical quantization

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Q. H. Liu, C. L. Tong, M. M. Lai. 2009-10-05. Constraint-induced mean curvature dependence of Cartesian momentum operators. https://doi.org/10.1088/1751-8113/40/15/007

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