Wednesday, September 12, 2012

1209.2209 (Q. H. Liu)

Geometric Momentum --- Angular Momentum Representation and Momentum
Spectrometer for some Molecular Rotational States

Q. H. Liu
For a free particle freely moving on a two-dimensional sphere or a free rotation of a spherical top, the projections of the geometric momentum $% \mathbf{p}$ and the angular momentum $\mathbf{L}$ onto a certain Cartesian axis are mutually commutable as $[L_{i},p_{i}]=0$ ($i=1,2,3$). We have therefore a geometric momentum -- angular momentum representation for the states on the two-dimensional spherical surface, whose basis vectors are simultaneous eigenstates of an operator pair, e.g., $(p_{z}$, $L_{z})$, and the representations determined by other pairs can be easily formed by coordinate rotations. The expression of the spherical harmonics in the new representation is explicitly carried out, and the geometric momentum distribution on some molecular rotational states seems within the resolution power of present momentum spectrometer.
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