Lect34_[Compatibility_Mode]

Lect34_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir 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 ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Six Ideas That Shaped Physics Unit Q, Chapters 10 and 11 Notices: Problem Set 11 is due next Monday before the beginning of ur last lecture session before Thanksgiving our last lecture session before Thanksgiving Midterm II at 8:00pm, Thursday, December 2 in MSEE B012
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atter Waves Matter Waves Last week during recitation we saw evidence that an electron beam with suitable kinetic energy diffract from crystals in the same way that x-rays do. omparing cases quantitatively reveals that in both cases the wave vector Comparing cases quantitatively reveals that in both cases the wave vector associated with the x-ray photons and with the electrons is related to their momenta by the deBroglie relation k G G pk = We’ve managed to reconcile the particle- and wave-like aspects of photons by introducing complex-valued representations of the corresponding electromagnetic fields that we can use to predict probabilities of detecting photons with different energies and momenta and in different locations at different times. In the case of the y -polarized cavity fields that we have studied most closely, () ( ) sin( ) 2 nn n n ik x ik x it yn n n n n n ee Ei i k x e i i e i ω αβ −− =− ∑∑ ^ py y , these probability wave amplitudes are ( ) cos( ) 2 ik x ik x zn n n n n cB i k x e i e + ^
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We have written them in the final form to emphasize that the fields propagating () ( ) sin( ) 2 nn n n ik x ik x it yn n n n n ee Ei i k x e i i e i ω αβ −− =− ∑∑ ^ freely within the cavity are plane waves ( ) cos( ) 2 ik x ik x zn n n n n cB i k x e i e + ^ hich as you will recall satisfy the wave equation for example in the case which, as you will recall, satisfy the wave equation, for example, in the case above 22 2 1 yy E E ct x ∂∂ = 2 1 zz BB x = and The is sufficient to assure that the particles associated with our probability wave amplitudes have the correct relationship between their energy and momentum to be photons, 2 2 2 2 2 1 E = 2 kk p cc c ω= ⇒== = = However, the electric and magnetic fields together must satisfy Maxwell’s quations to assure that photons have the correct internal structure (spin). equations to assure that photons have the correct internal structure (spin). The wave equation alone would govern probability amplitudes a hypothetical structureless photon.
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It seems natural to think that we can reconcile the particle- and wave-like behavior of massive particles be taking a similar approach.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue University.

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Lect34_[Compatibility_Mode] - Physics 344 Foundations of...

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