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arXiv · 1209.2209

Momentum spectrometry of spherical harmonics and a probe of geometric embedding effect

Q. H. Liu
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Abstract

As a submanifold is embedded into higher dimensional flat space, quantum mechanics gives various embedding quantities, e.g., the geometric momentum and geometric potential, etc. For a particle moving on a two-dimensional sphere or a free rotation of a spherical top, the projections of the geometric momentum p and the angular momentum L onto a certain Cartesian axis form a complete set of commuting observables as [p_{i},L_{i}]=0 (i=1,2,3). We have therefore a (p_{i},L_{i}) representation for the states on the two-dimensional spherical surface. The geometric momentum distribution of the ground states for a freely rotating rigid rotor seems within the resolution power of present momentum spectrometer and can be measured to probe the embedding effect.

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Q. H. Liu. 2013-02-25. Momentum spectrometry of spherical harmonics and a probe of geometric embedding effect. https://arxiv.org/abs/1209.2209

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