In Eq. 38-25 keep both terms, putting A B c0. The equation then describes the

Chapter 38, Problem 66

(choose chapter or problem)

In Eq. 38-25 keep both terms, putting A B c0. The equation then describes the superposition of two matter waves of equal amplitude, traveling in opposite directions. (Recall that this is the condition for a standing wave.) (a) Show that |(x, t)|2 is then given by |(x, t)|2 2 02[1 cos 2kx].k(b). Plot this function, and demonstrate that it describes the square of the amplitude of a standing matter wave. (c) Show that the nodes of this standing wave are located at x (2n 1)14 , where n 0, 1, 2, 3, . . . |and l is the de Broglie wavelength of the particle. (d) Write a similar expression for the most probable locations of the particle.