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Lecture33 - Physics 344 Foundations of 21st Century Physics...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 10 and 11 in the text. Exam 2: Thursday, December 1 at 8:00pm in ARMS B061
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Matter-Wave Mechanics After analyzing the diffraction of x-rays from a crystal during recitation this week, another instance of the wave-like behavior of photons, we saw evidence that electrons are also diffracted by crystals. Apparently, photons are not alone in possessing a dualistic wave-particle nature. Since we’ve developed a sophisticated quantum model of light that predicts and explains both the interference and photon-counting outcomes of experiments on electromagnetic field states, we come at the challenge of developing a quantum theory of electrons and other massive particles from a different perspective than the text does. Based on our experience working with the photon model we identified its essential features as Fundamental Principles of Quantum Mechanics that we can use to build a wave-mechanical model that explains and predicts both the interference and particle detection outcomes of experiments involving electrons and other massive particles. Last time, we discussed briefly how those Principles can be used to explain the electron behavior which the text discusses in chapter 6 to motivate accepting them.
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Q1. Is the wave function Ψ = Ψ (x) normalized? Note that this is a plot of | Ψ | 2 vs. x. * Q2. If the coefficient C 500 = 0.1+0.2 i in this wavefunction representing a specific single-photon state of the electromagnetic field in a cavity, what is the probability that when we detect the photon its energy will be ћω 500 ? A) 0.3 B) ½ C) 0.05 D) 0.01 E) -0.03+0.04 i ( 29 n=1 n=1 ( , ) ( ) ( ) n n i t i t n n n n n x t i x e c x e ϖ ϖ β α ψ ψ - - Ψ = - *
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The first electron-diffraction experiments of Thomson and of Davisson and Germer revealed interference patterns consistent with the de Broglie relation between electron momentum and wave vector p k = arrowrightnosp arrowrightnosp Since other particles do interfere and since we managed to explain particle- and wave-like photon behavior by introducing a wavefunction that predicts probabilities of the possible outcomes of measurements we can make of photon properties, it seems natural to try push the analogy between photons and massive particles further by introducing wavefunctions for electrons and other particles too. ( ( , ) sin( ) 2 n n n n ik x ik x i t i t n n n n n e e x t c k x e c e i ϖ ϖ - - - - Ψ = = For a polarized electromagnetic field state in a cavity, our photon wavefunction has the form (its real part is the state’s electric field amplitude) Recall that de Broglie suggested that all particles might exhibit interference
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