Open AccessThe Cartesian momentum and the kinetic operators on curved surfaces
Author(s) -
Quanhui Liu
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.674
Subject(s) - cartesian coordinate system , invariant (physics) , operator (biology) , kinetic energy , physics , curvature , orthogonal coordinates , classical mechanics , representation (politics) , momentum operator , coordinate system , momentum (technical analysis) , mathematical analysis , mathematical physics , mathematics , ladder operator , geometry , computer science , quantum mechanics , compact operator , chemistry , biochemistry , political science , transcription factor , programming language , finance , politics , economics , extension (predicate logic) , gene , repressor , law
For describing particles moving on the two dimensional curved surfaces, we can use either the intrinsic local coordinates or the Cartesian coordinates. The representation of the momentum operators differs from each other in these two kinds of coordinates, the former ones depend on the intrinsic geometrical quantities, but the latter case depend on a geometrical invariant, namely the mean curvature. Taking the operator-ordering problem into consideration, the kinetic operator for the former case can be expressed in a possibly unique way, while that for latter case can be expressed in two different ways.