Modern Physics

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PHY251 Homework Set 7 Reading: Chapter 8 Homework: Chapter 8, Question 1,4 Problems 1,6 Hints and Solutions Question VIII.1 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: No Solution yet Question VIII.4 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 π /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: No Solution yet
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Unformatted text preview: Problem VIII.1 A beam of electrons is sent along the x-axis from -∞ (infinity) with kinetic energy E = 4.2 eV. The beam encounters a potential barrier of height V = 3.2 eV and width 2 a = 1.2 nm. What fraction of the incident beam is reflected? Hints: No hints Solution: No Solution yet Problem VIII.6 Find an expression for the transmission coefficient of a particle with a fixed, finite energy phy251_hw07 (1 of 2) [3/28/2001 1:00:21 PM] approaching a barrier in the limiting case as V →∞ and a → 0 such that aV is a constant. What is | R | 2 ? Hints: You can simplify your algebra by defining a parameter λ ≡ k 2 a 2 . Solution: No Solution yet phy251_hw07 (2 of 2) [3/28/2001 1:00:21 PM]...
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