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# lecture5 - 5.61 F all 2007 Lecture#5 page 1 WAVE-PARTICLE...

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5.61 Fall 2007 Lecture #5 page 1 WAVE-PARTICLE DUALITY of LIGHT and MATTER (A) Light (electromagnetic radiation) Light as a wave For now we neglect the polarization vector orientation Propagating in x-direction: ξ 0 ξ 0 x (const. t ) or t (const. x ) ξ ( x , t ) = ξ 0 sin 2 π ( x ct ) λ 2 π Define k = (“wavevector” magnitude) λ At some fixed time, say t = 0, can write simply ξ x , t = 0 ) = ξ 0 ( ) ( sin kx Superposition principle sin( kx ) Constructive + = 2sin( kx ) interference sin( kx ) (in phase)

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5.61 Fall 2007 Lecture #5 page 2 sin( kx + π ) (out of phase by λ /2) This leads to many interference phenomena Young’s 2-slit experiment D λ = s λ D = s Light as a particle Compton exp’t If just a wave, expect light to scatter off electron Experimentally: e- x-rays ( λ 1 Å ) e- λ λ e- λ′ λ Destructive + = 0 interference sin( kx ) light, λ s l D Interference pattern screen observed
att ce 5.61 Fall 2007 Lecture #5 page 3 The backscattered wave is red-shifted ( λ > λ ), i.e. less energy/photon. hc hc E = < = E λ λ Energy (and momentum) transferred to the electron. Need relativistic mechanics to solve

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