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Geometric Momentum for a Particle on a Curved Surface | Q. H. Liu
; | Rating: | Visitors:    5/5 (1 visitor) | Date: |
1 Sep 2011 | Abstract: | When a two-dimensional curved surface is conceived as a limiting case of a
curved shell of equal thickness d, where the limit d
ightarrow0 is then taken,
the well-known 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 so-called geometric momentum instead. This momentum is
compatible with the Dirac’s canonical quantization theory on system with
second-class 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}. | Source: | arXiv, 1109.0153 | Services: | Forum | Review | PDF | Favorites |
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