Answer
Figure 38-18 shows a plot of the probability densities in the three regions. The oscillating curve to the left of the barrier (for $x \lt 0$) is a combination of the incident matter wave and the reflected matter wave. The oscillations occur because these two waves, traveling in opposite directions, interfere with each other, setting up a standing wave pattern. The amplitude of both incident matter wave and reflected matter wave has non zero value. In fact, the amplitude of reflected matter wave is smaller than that of the incident wave. Therefore, when they interfere with each other, the amplitude of resultant matter wave never becomes zero. The probability density is numerically equals to the square of the amplitude. Therefore, the minima of probability density in the left side of figure 38-18 are nonzero.
Work Step by Step
Figure 38-18 shows a plot of the probability densities in the three regions. The oscillating curve to the left of the barrier (for $x \lt 0$) is a combination of the incident matter wave and the reflected matter wave. The oscillations occur because these two waves, traveling in opposite directions, interfere with each other, setting up a standing wave pattern. The amplitude of both incident matter wave and reflected matter wave has non zero value. In fact, the amplitude of reflected matter wave is smaller than that of the incident wave. Therefore, when they interfere with each other, the amplitude of resultant matter wave never becomes zero. The probability density is numerically equals to the square of the amplitude. Therefore, the minima of probability density in the left side of figure 38-18 are nonzero.
