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Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface
Date
2018-09-01
Author
Shikakhwa, M. S.
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The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so "apparently" not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates. The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.
Subject Keywords
Physics and Astronomy (miscellaneous)
URI
https://hdl.handle.net/11511/63608
Journal
COMMUNICATIONS IN THEORETICAL PHYSICS
DOI
https://doi.org/10.1088/0253-6102/70/3/263
Collections
Department of Physics, Article
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M. S. Shikakhwa, “Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface,”
COMMUNICATIONS IN THEORETICAL PHYSICS
, pp. 263–267, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63608.