Distribution of xp in some molecular rotational states

• The posmom is defined on the two-dimensional spherical surface, and its relation with the geometric momentum is demonstrated.
• A new complete set on the surface is found and the spherical harmonics goes posmometry analysis.
• The embedding of the two-dimensional spherical surface S2S2 in three-dimensional flat space R3R3 is physically appealing.

Developing the analysis of the distribution of the so-called posmom xp to some molecular rotational states for diatomic molecules and spherical cage molecules, we obtain posmometry (introduced recently by Bernard and Gill, 2010 [5]) of the spherical harmonics and demonstrate that it is similar to the momentum distributions of the stationary states for a one-dimensional simple harmonic oscillator. The results are not only potentially experimentally testable but also reflect a fact that the embedding of the two-dimensional spherical surface S2S2 in three-dimensional flat space R3R3 is physically self-consistent and appealing.