3. A plane wave of energy E encounters a potential step of Ug. E U(x) (1) Uo (2) Calculate the transmission T and the reflection R probability when (a) Uo = }E. (b) Uo = 0. (c) Uo = E %3D
3. A plane wave of energy E encounters a potential step of Ug. E U(x) (1) Uo (2) Calculate the transmission T and the reflection R probability when (a) Uo = }E. (b) Uo = 0. (c) Uo = E %3D
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Transcribed Image Text:**Potential Step Problem**
3. A plane wave of energy \( E \) encounters a potential step of \( U_0 \).
**Diagram Explanation:**
- The diagram consists of a horizontal axis labeled \( x \).
- The potential energy, \( U(x) \), is shown as a step function:
- For region (1), \( U(x) \) is constant at 0.
- At the point of transition, the potential energy steps up to \( U_0 \) in region (2).
- The energy \( E \) of the wave is represented with a horizontal dashed line, which lies above the potential step at \( U_0 \).
- An arrow indicates the step change in potential.
**Problem Statement:**
Calculate the transmission (\( T \)) and the reflection (\( R \)) probabilities when:
(a) \( U_0 = \frac{1}{2} E \).
(b) \( U_0 = 0 \).
(c) \( U_0 = E \).
Expert Solution
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The transmission T and the reflection R probability is given by
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