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.