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We in the definition of a continuous function of time in . assume that our Therefore each term of the (fo, t). a continuous function of time. The generator S must, because of continuity, have a maximum in (zfo, t). The orthogonality condition A*A series is AA* = I must be satisfied during (>, f). From tr (A*A) = tr I = = Vn. 6) This condition of the norm can be incorporated into the proof of convergence of the series. We have tr (A^A\AiA) = tr A\Ai. 7) leads to 1 to AW + ^ v-. B. Symbolic Expression for a General Time-Dependent Rotation Operator Consider the term A, * = A 2 of the series (-*o 2 r r e+ & ^ y to j + ^, ^scosfe) (% <%.

There are, in general, various methods available for solving integral equations. For the present problem we shall use Neumann-Liouville's "method of successive substitutions/' the iteration method. 3), in place of A(ti } to), its value find (- + (-i) 2 r r e+(t, Jto Jlo where the limits of the integrals are, because of e + function, the same. Continuthe of substitution we obtain ing process A(t, fe) - I + (-i) f' Jto +(t, tdSfa) dk l + (-i? ( f'dtidtt^t, feKfe, fe)S(fc)Sfe) + + (-i) n [' ... [* dk dtn X S(ti) S(tn + JtQ Jfo - e+(t, fe) JtQ JtO ) +!.

What is the general nature of a system unaffected by such transformations? 2. Prove that a spherically symmetric function F does not change under an infinitesimal transformation of coordinates, regardless of the nature of the generator of the transformation. Conversely, any function remaining unchanged under any infinitesimal change of coordinates is a spherically sym- metric function of coordinates. 3. 28) is taken to be the Lagrangian of a dynamical system, then the Lagrangian does not change if the total angular momentum is conserved and the angular momentum vector can be a function of time.

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