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Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices
Authors:M. L. Ellzey Jr.
Affiliation:(1) Department of Chemistry, The University of Texas at El Paso, 79968-0513 El Paso, TX, USA
Abstract:TheSU(2) rotation matricesD(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.
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