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e potential energy barrier

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(a) Write down the wave functions for the three regions of the potential energy barrier (Figure 5.25) for E < U₁. You will need six coefficients in all. Use complex exponential notation. (b) Use the boundary conditions at x = 0 and at 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?
Transcribed Image Text:(a) Write down the wave functions for the three regions of the potential energy barrier (Figure 5.25) for E < U₁. You will need six coefficients in all. Use complex exponential notation. (b) Use the boundary conditions at x = 0 and at 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. mm www 1412 (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 for E< U. The probability density and the real and imaginary parts of the wavefunction are shown for (a) t = 0 and (b) t = 1/4 period. The vertical line marks the location of the step.
Transcribed Image Text:www. mm www 1412 (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 for E< U. The probability density and the real and imaginary parts of the wavefunction are shown for (a) t = 0 and (b) t = 1/4 period. The vertical line marks the location of the step.
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