Constraint-induced mean curvature dependence of Cartesian momentum operators

Details Constraint-induced mean curvature dependence of Cartesian momentum operators Constraint-induced mean curvature dependence of Cartesian momentum operators

2009-10-05

arxiv.org/abs/0910.0769v1

J. Phys. A: Math. Theor. 40 (2007) 4161

Physics

Mathematical Physics

7 pages. Revtex

Scientific paper

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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