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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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**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) \( U_0 = E \).
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) \( U_0 = E \).
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The transmission T and the reflection R probability is given by

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