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Lecture28 - 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: Sections 1.3 through 1.6 and Chapters 4 and 5 in Six Ideas that Shaped Physics, Unit Q
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Question 1. An atom at rest in inertial coordinate system S emits a photon with angular frequency ω in the y direction. What frequency does an S’ frame observer measure this photon to have? Use SR units and assume that S’ moves at speed V relative to the Home frame and is in standard orientation relative to it. A) B) C) D) 0 0 0 0 0 0 1 0 0 0 0 1 t V t x V x y y z z γ γ γ γ -     -   =       ϖ γϖ (1 ) V γ ϖ - (1 ) V γ ϖ Answer: In conventional units so in SR units . 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 x y z V k V V k k ϖ γϖ γ γ ϖ γ ϖ γ γ ϖ ϖ -     - -   = =       kc ϖ = k ϖ = from which we read ϖ γϖ = Note that the negative x component of the photon’s wave vector in the Other frame is consistent with our comments about the headlight effect. Hint: In the homework problem involving the Doppler effect, the emitting atoms are at rest in one frame but the direction in which the photons of interest propagate is specified in the other frame. Also, the stars’ velocities in Newtonian orbits are small enough to approximate . 1 γ
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x L d << L 1 k arrowrightnosp 1 2 2 k arrowrightnosp screen In single-photon multi-slit interference experiments, we are unable to predict any specific detection event, yet interference fringes emerge as we repeat the experiment many times. The way in which quantum mechanics explains these outcomes is by invoking a wavefunction (state vector) that represents any single-photon state but having this wavefunction carry only information about the probability of detecting a photon at a particular place and time or with a particular energy or momentum. Since interference patterns consistent with the wave model of light emerge, quantum wavefunctions must have forms that are closely related to the classical wave fields we’ve been analyzing. z
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x L d << L 1 k arrowrightnosp 1 2 2 k arrowrightnosp screen z 1 2 ( , ) cos( ) cos( ) y E r t E k r t E k r t ϖ ϖ - + - arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp 1 2 1, 0, 2 d k L π λ arrowrightnosp 2 2 1, 0, 2 d k L π λ - arrowrightnosp 2 ( , )=2 cos cos y d x E r t E z t L π π ϖ λ λ - arrowrightnosp and
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