S C McFarlane 1992 J. Phys. B: At. Mol. Opt. Phys. 25 4045 doi:10.1088/0953-4075/25/20/004
Angular momentum and Heisenberg's correspondence principle
S C McFarlane
Show affiliationsHeisenberg's form of the correspondence principle is applied to the matrix elements of tensor operators. A correspondence limit of the Wigner-Eckart theorem is obtained. It is shown that the Clebsch-Gordan coefficient tends in this limit to the product of a reduced rotation matrix element with a simple multiplicative factor. A similar, but not identical, expression has long been known as a formal limit obtaining when two of the three angular momenta involved become large. It is characteristic of correspondence principle expressions that the initial and final quantal states must be represented by some 'mean' classical orbit, the choice of which remains ambiguous. Here recursion relations are used to arrive at the optimal choice. In this way, a correspondence principle approximation to the Clebsch-Gordan coefficient is obtained which may be used with success far from the limit to which it nominally refers. This approximation is tested numerically against both exact and semiclassical computations.
- PACS
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31.15.xg Semiclassical methods
- MSC
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47A80 Tensor products of operators (See also 46M05)
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 20 (28 October 1992)
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Angular momentum and Heisenberg's correspondence principle
S C McFarlane 1992 J. Phys. B: At. Mol. Opt. Phys. 25 4045
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