After transmission through the barrier the energy is

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2 3. After transmission through the barrier, the energy is the same. correct 4. After transmission through the barrier, the wavelength is smaller. 5. After transmission through the barrier, the wavelength is greater. Explanation: It is essential to recognize that the only thing that changes as you modify the shape of the barrier is the transmission probability, i.e. the number of particles that will get through. Therefore only the amplitude will change as you modify the shape of the barrier; the energy will always remain the same. tween a and b ), what would happen to the transmission probability?
005(part4of4)10.0points Varying which of the following will increase the wavelength of the transmitted wave? With everything else held fixed, if we dou- ble the height of the barrier U ( x ), what will happen to the transmission probability? 1. More information is required. 2. It will decrease. correct 3. It will stay the same. 4. It will increase. Explanation: Since for tunneling we assume that E < U ( x ), doubling the height of the barrier will increase the absolute value of the integrand, and therefore will decrease the probability of transmission. This also makes sense in- tuitively, since a higher barrier presents a greater obstacle (note that for an infinitely high barrier, the transmission probability drops to zero). 006(part1of4)10.0points Recall the approximate formula for transmis- sion through an arbitrary barrier from the 007(part2of4)10.0points With everything else held fixed, if we dou- ble the height of the barrier U ( x ), what will happen to the transmission probability?
video: integraldisplay b a vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle radicalbig 2 m ( E - U ( x )) ¯ h vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle dx .
Keeping everything else the same, if you dou- ble the width of the barrier (the distance be-

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