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Since 1 < n < N this error has TV components. Suppose that the system has N linearly independent eigenfunctions. Then we can write ε{0)(η) as a sum of the TV linearly independent eigenfunctions: ε<°>(/ι) = Σ βιβι(η) (19) Z=i After one cycle we have according to (17), (18), and (19) ε«>(/ι) = Σ <χΛ(0,(/0 = Σ Σ ßiajetk) = Σ ßM(«) k=l Z=l k=l 1=1 Each eigenfunction is multiplied by a factor equal to its eigenvalue. After m cycles £(m)(n) = Σ ß^efr) (20) /=1 If | λχ I < 1 this iteration procedure converges to the final solution e{co)(n) = 0.

2. For dynamics of particles: Corben, H. C. and Stehle, P. (1960). " Wiley, New York. De Broglie, L. (1950). " Hermann, Paris. Glaser, W. (1952). " Springer, Berlin. Goldstein, H. (1959). " Addison-Wesley, Reading, Massachussetts. Landau, L. , and Lifshitz, E. M. (1961). " Macmillan (Pergamon), New York. Pierce, J. R. (1949). " Van Nostrand, Princeton, New Jersey. A. (1955). " Cambridge Univ. Press, London and New York. von Ardenne, M. (1955). " VEB Deutscher der Wissenschaften, Berlin. Whittaker, E.

46) These integrals will be evaluated on four-dimensional or two-dimensional surfaces of phase-space. 47) The integration path is now, in the geometrical space, a closed curve encircling all the trajectories. 49) where ψΒ is the magnetic flux across the closed curve that is used for integration. 1 PARTICLES AND FIELDS! 51) In the case of fields independent of time, H is equal to the sum of kinetic energy and potential energy; it is constant. 4. Particle Beams A. PERTURBATIONS METHOD Now, we shall study the perturbations method, which is the basis of corpuscular focusing.

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