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Consider the "step" potential: 0, { (a) Calculate the reflection coefficient, for the case E< Vo., and comment on the answer. if x ≤ 0. Vo. if x > 0. V(x) = (b) Calculate the reflection coefficient for the case E> Vo. (c) For a potential such as this, which does not go back to zero to the right of the barrier, the transmission coefficient is not simply |F12/A2 (with A the

Consider the "step" potential: 0, { (a) Calculate the reflection coefficient, for the case E< Vo., and comment on the answer. if x ≤ 0. Vo. if x > 0. V(x) = (b) Calculate the reflection coefficient for the case E> Vo. (c) For a potential such as this, which does not go back to zero to the right of the barrier, the transmission coefficient is not simply |F12/A2 (with A the

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Consider the "step" potential: V(x) = (a) Calculate the reflection coefficient, for the case E< Vo, and comment on the answer. 0. if x ≤ 0. Vo. if x > 0. (b) Calculate the reflection coefficient for the case E > Vo. (c) For a potential such as this, which does not go back to zero to the right of the barrier, the transmission coefficient is not simply |F12/A2 (with A the -Vo AV(x) Scattering from a "cliff" incident amplitude and F the transmitted amplitude), because the transmitted wave travels at a different speed. Show that T = E-Vo F1² E |A|² X for E> Vo. Hint: You can figure it out using Equation gantly, but less informatively-from the probability current ( What is T, for E < Vo? -or-more ele- (d) For E> Vo, calculate the transmission coefficient for the step potential, and check that T + R = 1.
Transcribed Image Text:Consider the "step" potential: V(x) = (a) Calculate the reflection coefficient, for the case E< Vo, and comment on the answer. 0. if x ≤ 0. Vo. if x > 0. (b) Calculate the reflection coefficient for the case E > Vo. (c) For a potential such as this, which does not go back to zero to the right of the barrier, the transmission coefficient is not simply |F12/A2 (with A the -Vo AV(x) Scattering from a "cliff" incident amplitude and F the transmitted amplitude), because the transmitted wave travels at a different speed. Show that T = E-Vo F1² E |A|² X for E> Vo. Hint: You can figure it out using Equation gantly, but less informatively-from the probability current ( What is T, for E < Vo? -or-more ele- (d) For E> Vo, calculate the transmission coefficient for the step potential, and check that T + R = 1.
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