In Eq.38-18 keep both terms, putting A - B ? ?₀ 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 are then given by |? (x, t)|² = 2?²_0?[1 + cos 2kx].

(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) (? ?), where n = 0, 1, 2, 3 and ? [ is the de Broglie wavelength of the particle.?

(d) Write a similar expression for the most probable locations of the particle.

V(x, t)? = 20[1 + cos 2kx]. (2n + 1)GA). where n = 0, 1, 2, 3,... %3D