By Brain Judd (Auth.)

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M) 1 Assemble these results to prove Eq. 25). (μ) * (μ * COS χ ) 2 by C V ' ( c o s χ ) sin χ άχ and integrating over χ, prove that the coefficient of h'gff in f (1 - *\ - 2μh + -2ug 2 1 + β·)-»(1 - 2M/ + / ) - <*M -1 9 is £τΔ(#'β). Show that this is equal to the coefficient of hWf in and deduce that Δ(#'β) = 1 if tt t', and s satisfy the triangular condition and if, in addition, t + t' + β is even: otherwise A(Ufa) = 0. 5 Derive Eq. 1 THE RIGID ROTATOR The notion of a rigid rotator is an abstraction.

21). The partial derivatives Β/Βξ, Β/Βη, and Β/Βξ that occur here carry the implication that the quaternion r is constant; so we have merely to relate these derivatives t o those of the type B/BXa by means of Eq. 10). , and f of p. This can be readily understood, since (XIXIX&A) lies on the unit sphere in four dimen­ sions. From a formal point of view, however, we need to augment ρ by one variable. This is easily done by defining Ρ - e + i{ + j , , + kf. Several other preliminary statements need to be made.

LM) and sums over m and m! are performed. 30) A similar procedure is available for Λ ( 4 ) . As Talman [ 2 9 ] shows, analogs of the 3D functions can be found, and they too can be made to reduce to F N I M( G ) . It seems preferable, however, to take the opportunity of illustrating a different method. As a preliminary to this, we note that the dependence on m, m\ and m" of the coefficient in Eq. 29) is simply a C G coefficient. This must be so, since the m quantum numbers are the 2 38 The Rotation Group R(4) component labels of tensors, a n d t h e correct coupling m u s t be exhibited.

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Angular Momentum Theory for Diatomic Molecules by Brain Judd (Auth.)
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