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

2012/09/11 by Liu, Q. H.
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1209.2209

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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