Lecture28 - Physics 344 Foundations of 21 st Century...

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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Fan Chen Office: PHYS 222 chen926@purdue.edu 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 Question 1. An atom at rest in inertial coordinate system S emits a photon with angular frequency 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) 1 1 t V t x V x y y z z - - = (1 ) V - (1 ) V + Answer: In conventional units so in SR units . 1 1 x y z V k V V k k - -- = = kc = k = from which we read = Note that the negative x component of the photons 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 x L d << L 1 k a 1 2 2 k a 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 weve been analyzing. z x L d << L 1 k a 1 2 2 k a screen z 1 2 ( , ) cos( ) cos( ) y E r t E k r t E k r t - + - a a a a a 1 2 1, 0, 2 d k L a 2 2 1, 0, 2 d k L - a 2 ( , )=2 cos cos y d x E r t E z t L - a and The former highlights the way in which the field is understood as a superposition of plane waves that we associate with...
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This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue University-West Lafayette.

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Lecture28 - Physics 344 Foundations of 21 st Century...

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