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Workshop on Geometric Methods in Physics (WGMP)

GREEN'S FUNCTION FOR CROSSED TIME-DEPENDENT ELECTRIC AND MAGNETIC FIELDS PHASE-SPACE QUANTUM MECHANICS APPROACH

Luis Miguel Nieto

Published Oct 1, 1993• 1 citation
Publisher
DOI
10.1142/9789814440844_0024

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International Journal of Modern Physics A•Jul 30, 2010•2 citations
The excitation spectrum of atomic sodium in crossed electric and magnetic fields has been recorded. Data for states near n = 11 are found to be in good agreement with theoretical estimates of line positions. The agreement with estimates of line strengths, however, is only fair. The lack of complete agreement between simple hydrogenic theory and experiment can be traced t o a breakdown of the assumption that the influence of the nearby 12p state is negligibly small. The significance of this experiment is that, for the first time, clear evidence of m-mixing between bound states has been obtained. The dominant effect of the m-mixing has been to make accessible optically many Rydberg states. These states in the presence of electric or magnetic fields alone would not have been accessible because of selection rules on m.
In relation to the current controversy over the need for an experimental test of spatial noncommutativity at the normal quantum scale, the spectra of a Rydberg electron in the vicinity of the saddle-point in a suitable combination of crossed electric and magnetic fields are investigated in both cases of commutative space and noncommutative space. Its local behavior around the saddle-point is clarified. An unbounded mode is revealed. It describes the unbounded direction along which the electron will escape the vicinity of the saddle-point, which means that it is impossible to locate electronic states. This finding indicates that the possibility of testing spatial noncommutativity in the vicinity of the saddle-point is ruled out. Because this unbounded mode applies only to states near the saddle-point, not to those from the outer well, it is suggested that if any test of spatial noncommutativity can be performed by using atoms in the crossed-field, then the test must be performed using states from the outer well, not those close to the saddle-point.