
Physics 2011
Geometric Momentum for a Particle on a Curved SurfaceAbstract: When a twodimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the wellknown geometric potential is induced by the kinetic energy operator, in fact by the second order partial derivatives. Applying this confining procedure to the momentum operator, in fact to the first order partial derivatives, we find the socalled geometric momentum instead. This momentum is compatible with the Dirac's canonical quantization theory on system with secondclass constraints. The distribution amplitudes of the geometric momentum on the spherical harmonics are analytically determined, and they are experimentally testable for rotational states of spherical molecules such as C_{60}.
