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Journal of Mathematical Physics

The intelligent states. II. The computation of the Clebsch–Gordan coefficients

M. A. Rashid

Published Jun 1, 1978• 16 citations
Publisher

Abstract

In this second of a series of papers on quasi-intelligent states, we give a general method for the computation of the Clebsch–Gordan coefficients for these states. In a special case, these coefficients are found to be closely related to the Clebsch–Gordan coefficients of the rotation group. We also discuss the nonuniqueness resulting naturally from the overcompleteness of these states.

DOI
10.1063/1.523841

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In this second of a series of papers on quasi-intelligent states, we give a general method for the computation of the Clebsch–Gordan coefficients for these states. In a special case, these coefficients are found to be closely related to the Clebsch–Gordan coefficients of the rotation group. We also discuss the nonuniqueness resulting naturally from the overcompleteness of these states.
In this first of a series of papers, a group-theoretic study is presented of the quasi-intelligent states which are a generalization of the intelligent states satisfying equality in the Heisenberg uncertainty relation ΔJ12ΔJ22? (1/4) ‖〈J3〉‖2. A method based on the knowledge of a certain generating function is given for the calculation of matrix elements of polynomials in the infinitesimal generators of the rotation group between quasi-intelligent states. Examples of such computations are also included to exhibit the improvement and efficiency of the present methods.