Journal
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
Volume 82, Issue 10, Pages -Publisher
PHYSICAL SOC JAPAN
DOI: 10.7566/JPSJ.82.104002
Keywords
constrained systems; embedding effects; geometric momentum; dynamical representation on sphere; momentum spectrometry; mean curvature
Categories
Funding
- National Natural Science Foundation of China [11175063]
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As a manifold is embedded into a higher dimensional Euclidean space, quantum mechanics gives various embedding quantities. In the present study, two embedding quantities for a two-dimensional curved surface in the three-dimensional flat space, the geometric momentum and the geometric potential, are derived in a unified manner. For a particle moving on a two-dimensional sphere or a free rotation of a spherical top, the projections of both 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), thus constituting a dynamical (p(i), L-i) representation for the states on the two-dimensional spherical surface. The geometric momentum distribution of the states represented by spherical harmonics is successfully obtained, and this distribution for a homonuclear diatomic molecule seems within the resolution power of present momentum spectrometers and can be measured to probe the embedding effect.
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