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Unformatted text preview: PHY251 Homework Set 7 Reading: Chapter 8 Homework: Chapter 8, Question 1,4 Problems 1,6 Hints and Solutions Question VIII.1 (10 points) In the wavefunction that describes a particle colliding with a barrier in one dimension we have elements that describe momenta going in opposite directions in the same wave function. Does this mean that the particle "does not know what it is doing"? What is the probability interpretation of this wave function? Hints: No hints Solution: These elements do describe particles that move in opposite direction: once squared they signify the probability of finding a reflected particle in "front" of the barrier, and of finding a particle transmitted "behind" the barrier. Any given electron will either reflect r be transmitted (never both!), and the squared components of the wavefunction describe the probabilities for these alternatives to happen. Question VIII.4 (10 points) In the study of transmission across a square barrier, one finds in Eq. (8-12) that the barrier does not reflect when sin2 qa = 0 -- that is, when qa = n /2 for n a positive integer. Give a physical explanation of how this perfect transmission is achieved. Can you think of a practical application of the phenomenon?. Hints: Attempt this question after solving problem 6 . Solution: In this case we study the situation when E V , see equation 8-12. The reflection probability contains the factor sin(2 aq ), where q [ 2 m ( E- V )]/ h = 2 / is the wave number of the wave function...
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