(a) Write down the wave functions for the three regions ofthe potential energy barrier (Figure 5.25) for E < U₁. Youwill need six coefficients in all. Use complex exponentialnotation. (b) Use the boundary conditions at x = 0 andat x = L to find four relationships among the six coeffi-cients. (Do not try to solve these relationships.) (c) Sup-pose particles are incident on the barrier from the left.Which coefficient should be set to zero? Why? www. mmwww1412(a)Re(y)Re(y)Im(y)(b)Im(y)FIGURE 5.25 Wave function for electrons incident from the left on a potential energy step forE< U. The probability density and the real and imaginary parts of the wavefunction are shownfor (a) t = 0 and (b) t = 1/4 period. The vertical line marks the location of the step.

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