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SECTION B Answer TWO questions from Section B Question B1 Consider a finite potential step as shown below, with V = V in the region x < 0 and V = 0 in the region x 0. Particles with energy E 0. Identify which part of your solution corresponds to a left-moving wave, and which part corresponds to a right-moving wave. [4 marks] Write down and solve the time-independent Schrödinger equation in the region x < 0. Explain the condition that should obey at x → ∞, and use this to set one of the terms b) in your solution to zero. c) [4 marks] Write down the boundary conditions that & must obey at x = 0, and use your solutions from parts a) and b) to evaluate them in the present case. [4 marks] d) Give a general definition for the probability current j, and use your definition to calculate the incident and reflected probability currents for the situation described above. [6 marks] e) Use your answers from questions c) and d) to determine the value of the reflection coeffi- cient R for the situation described above. What is the value of the transmisson coefficient T in this case? [7 marks]

SECTION B Answer TWO questions from Section B Question B1 Consider a finite potential step as shown below, with V = V in the region x < 0 and V = 0 in the region x 0. Particles with energy E 0. Identify which part of your solution corresponds to a left-moving wave, and which part corresponds to a right-moving wave. [4 marks] Write down and solve the time-independent Schrödinger equation in the region x < 0. Explain the condition that should obey at x → ∞, and use this to set one of the terms b) in your solution to zero. c) [4 marks] Write down the boundary conditions that & must obey at x = 0, and use your solutions from parts a) and b) to evaluate them in the present case. [4 marks] d) Give a general definition for the probability current j, and use your definition to calculate the incident and reflected probability currents for the situation described above. [6 marks] e) Use your answers from questions c) and d) to determine the value of the reflection coeffi- cient R for the situation described above. What is the value of the transmisson coefficient T in this case? [7 marks]

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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SECTION B Answer TWO questions from Section B Question B1 Consider a finite potential step as shown below, with V = V in the region x < 0 and V = 0 in the region x 0. Particles with energy E<V are incident on this barrier from the right-hand side. V(x) Vo a) O<E<Vo X 0 Figure 1: A finite potential step, with particles incident from the right. Write down and solve the time-independent Schrödinger equation in the region x > 0. Identify which part of your solution corresponds to a left-moving wave, and which part corresponds to a right-moving wave. [4 marks] Write down and solve the time-independent Schrödinger equation in the region x < 0. Explain the condition that should obey at x → ∞, and use this to set one of the terms b) in your solution to zero. c) [4 marks] Write down the boundary conditions that & must obey at x = 0, and use your solutions from parts a) and b) to evaluate them in the present case. [4 marks] d) Give a general definition for the probability current j, and use your definition to calculate the incident and reflected probability currents for the situation described above. [6 marks] e) Use your answers from questions c) and d) to determine the value of the reflection coeffi- cient R for the situation described above. What is the value of the transmisson coefficient T in this case? [7 marks]
Transcribed Image Text:SECTION B Answer TWO questions from Section B Question B1 Consider a finite potential step as shown below, with V = V in the region x < 0 and V = 0 in the region x 0. Particles with energy E<V are incident on this barrier from the right-hand side. V(x) Vo a) O<E<Vo X 0 Figure 1: A finite potential step, with particles incident from the right. Write down and solve the time-independent Schrödinger equation in the region x > 0. Identify which part of your solution corresponds to a left-moving wave, and which part corresponds to a right-moving wave. [4 marks] Write down and solve the time-independent Schrödinger equation in the region x < 0. Explain the condition that should obey at x → ∞, and use this to set one of the terms b) in your solution to zero. c) [4 marks] Write down the boundary conditions that & must obey at x = 0, and use your solutions from parts a) and b) to evaluate them in the present case. [4 marks] d) Give a general definition for the probability current j, and use your definition to calculate the incident and reflected probability currents for the situation described above. [6 marks] e) Use your answers from questions c) and d) to determine the value of the reflection coeffi- cient R for the situation described above. What is the value of the transmisson coefficient T in this case? [7 marks]
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