Lect28_[Compatibility_Mode]

Lect28_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and Their Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! appointment. Notices: Midterm II at 8:00pm, Thursday, December 2 in MSEE B012
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From the beginning of your study of electromagnetic physics M&I has emphasized the fundamental role of field superposition. Using what Maxwell’s equations tell us about the structure of monochromatic plane waves we were able to understand the interference phenomena we i d f iti examined as consequences of superposition. We’ve noted the tension between the wave-model account of such phenomena, with its smooth flow of energy represented by the cycle-averaged Poynting vector, and the discreteness of photon-counting measurements of those flows made possible by the photoelectric effect. We’ve also hinted that resolving this tension and blending the wave and photon models of light requires that we think of the electromagnetic wave fields as somehow telling us about the we think of the electromagnetic wave fields as, somehow, telling us about the probability that an observer with a photomultiplier tube will detect photons at different locations and times. It is simplest to develop this blended quantum theory by considering photons It is simplest to develop this blended quantum theory by considering photons confined in a cavity formed by reflecting surfaces. We begin by examining the structure of the standing-wave fields that correspond to these states of the electromagnetic field Once again this is a consequence to these states of the electromagnetic field. Once again, this is a consequence of superposition, this time of counter-propagating monochromatic plane waves.
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Question 1. An atom at rest in a Home frame emits a photon with angular frequency ω in the y direction. What frequency does an Other frame observer measure this photon to have? Use SR units and assume that the Other frame moves at speed V relative to the Home frame and is in standard orientation relative to it ⎤ ⎡ relative to it. A) B) C) D) 0 0 0 0 0 0 1 0 t V t x V x y y γ γ γ γ Δ Δ ⎥ ⎢ Δ Δ ⎥ ⎢ = ⎥ ⎢ Δ Δ ⎥ ⎢ ω γω (1 ) V γ ω (1 ) V γ ω + C) D) 0 0 0 1 z z Δ Δ ⎦ ⎣ Answer: In conventional units so in SR units . kc ω = k ω = 0 0 0 0 0 0 0 1 0 x V k V V k ω γω γ γ ω γ ω γ γ ω ω ⎤ ⎡ ⎥ ⎢ ⎥ ⎢ = = ⎥ ⎢ from which we read ω γω 0 0 0 0 1 0 y z k ⎥ ⎢ ⎦ ⎣ = Note that the negative x component of the photon’s wave vector in the Other frame is consistent with our discussion of the headlight effect.
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