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Suppose a large number of particles are bouncing back and forth between x = 0 and x = l, except that at each endpoint some escape. Let r be the fraction reflected each time; then (l â€” r) is the fraction escaping. the particles start at x = 0 heading toward x = 1; eventually all particles will escape. Write an infinite series for the fraction which escape at x = 1 and similarly for the fraction which escape at x = 0. Sum both the series. What is the largest fraction of the particles which can escape at x = 0? (Remember that r must be between 0 and 1.)

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# Chapter 1 Solutions

Mathematical Methods in the Physical Sciences

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