In the equation for the time-dependent wave function I ( x, t) = V(x)e int - Aci(kx-wt) + Be i(katut) keep both terms, putting A = B = Vo. 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) Find IT (x, t) 12. IT ( 20, t ) 12 = (b) Find the positions of the nodes of this standing wave in terms of 1, the de Broglie wavelength of the particle. C = (c) Find a similar expression for the most probable locations of the particle. OC = ? 57