For a particle moves on a 2D surface f (x) = 0 embedded in 3D Euclidean space, the geometric momentum and potential are simultaneously admissible within the Dirac canonical quantization scheme for constrained motion. In our approach, not the full scheme but the symmetries indicated
Developing the analysis of the distribution of the so-called posmom xp to the
spherical harmonics that represents some molecular rotational states for such
as diatomic molecules and spherical cage molecules, we obtain posmometry
(introduced recently by Y. A. Bernard and P. M. W. Gill, Posmom: The Unobserved
Observable, J. Phys. Chem. Lett. 1(2010)1254) of the spherical harmonics and
demonstrate that it bears a striking resemblance to the momentum distributions
of the stationary states for a one-dimensional simple harmonic oscillator.Comment: 8 pages, 3 figure
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