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4.5 Consider reflection from a step potential of height Vo with E > Vo, but now with an infinitely high wall added at a distance a from the step (see diagram): V(x) E V = Vo V = 0 x = 0 x = a x (a) Solve the Schrödinger equation to find v/(x) for x < 0 and 0 ≤ xa. Your solution should contain only one unknown constant. (b) Show that the reflection coefficient at x = 0 is R = 1. This is different from the value of R previously derived without the infinite wall. What is the physical reason that R = 1 in this case? (c) Which part of the wave function represents a leftward-moving particle at x < 0? Show that this part of the wave function is an Solutions of the one-dimensional time-independent Schrödinger equation 103 eigenfunction of the momentum operator, and calculate the eigen- value. Is the total wave function for x ≤ 0 an eigenfunction of the momentum operator?

4.5 Consider reflection from a step potential of height Vo with E > Vo, but now with an infinitely high wall added at a distance a from the step (see diagram): V(x) E V = Vo V = 0 x = 0 x = a x (a) Solve the Schrödinger equation to find v/(x) for x < 0 and 0 ≤ xa. Your solution should contain only one unknown constant. (b) Show that the reflection coefficient at x = 0 is R = 1. This is different from the value of R previously derived without the infinite wall. What is the physical reason that R = 1 in this case? (c) Which part of the wave function represents a leftward-moving particle at x < 0? Show that this part of the wave function is an Solutions of the one-dimensional time-independent Schrödinger equation 103 eigenfunction of the momentum operator, and calculate the eigen- value. Is the total wave function for x ≤ 0 an eigenfunction of the momentum operator?

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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4.5 Consider reflection from a step potential of height Vo with E > Vo, but now with an infinitely high wall added at a distance a from the step (see diagram): V(x) E V = Vo V = 0 x = 0 x = a x (a) Solve the Schrödinger equation to find v/(x) for x < 0 and 0 ≤ xa. Your solution should contain only one unknown constant. (b) Show that the reflection coefficient at x = 0 is R = 1. This is different from the value of R previously derived without the infinite wall. What is the physical reason that R = 1 in this case? (c) Which part of the wave function represents a leftward-moving particle at x < 0? Show that this part of the wave function is an Solutions of the one-dimensional time-independent Schrödinger equation 103 eigenfunction of the momentum operator, and calculate the eigen- value. Is the total wave function for x ≤ 0 an eigenfunction of the momentum operator?
Transcribed Image Text:4.5 Consider reflection from a step potential of height Vo with E > Vo, but now with an infinitely high wall added at a distance a from the step (see diagram): V(x) E V = Vo V = 0 x = 0 x = a x (a) Solve the Schrödinger equation to find v/(x) for x < 0 and 0 ≤ xa. Your solution should contain only one unknown constant. (b) Show that the reflection coefficient at x = 0 is R = 1. This is different from the value of R previously derived without the infinite wall. What is the physical reason that R = 1 in this case? (c) Which part of the wave function represents a leftward-moving particle at x < 0? Show that this part of the wave function is an Solutions of the one-dimensional time-independent Schrödinger equation 103 eigenfunction of the momentum operator, and calculate the eigen- value. Is the total wave function for x ≤ 0 an eigenfunction of the momentum operator?
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