Answer: A free particle moving in one dimension has wave

Chapter 40, Problem 40.2

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A free particle moving in one dimension has wave function 1x, t2 = A3ei1kx-vt2 - ei12kx-4vt2 4 where k and v are positive real constants. (a) At t = 0 what are the two smallest positive values of x for which the probability function 0 1x, t2 0 2 is a maximum? (b) Repeat part (a) for time t = 2p>v. (c) Calculate vav as the distance the maxima have moved divided by the elapsed time. Compare your result to the expression vav = 1v2 - v12>1k2 - k12 from Example 40.1

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