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: ξ0 ξ 0 x (const. t) or t (const. x) ⎡ 2π ⎤ ξ x,t = ξ0 sin ⎢ x − ct ⎥ ⎣λ ⎦ ( ) Define ( k= 2π λ ) (“wavevector” magnitude) ( ) ( ) At some fixed time, say t = 0, can write simply ξ x,t = 0 = ξ0 sin kx Superposition principle sin(kx) + sin(kx) (in phase) = 2sin(kx) Constructive interference 5.61 Fall 2007 Lecture #5 page 2 sin(kx) Destructive interference =0 + sin(kx + π) (out of phase by λ/2) This leads to many interference phenomena Young’s 2-slit experiment D l s light, λ Interference pattern observed screen D λ = l s ⇒ D= λl s Light as a particle Compton exp’t e- x-rays (λ ∼ 1Å) If just a wave, expect light to scatter off electron e- λ Experimentally: λ e- λ′ λ 5.61 Fall 2007 Lecture #5 page 3 The backscattered wave is red-shifted ( λ ′ > λ ), i.e. less energy/photon. E′ = hc hc < =E λ′ λ Energy (and momentum) transferred to the electron. Need relativistic mechanics to solve p= Light is a particle with hν ⎛ h ⎞ = c ⎜⎝ λ ⎟⎠ for the light Ehν= energy momentum p= hν c Light can behave both as a wave and as a particle!! Which aspect is observed depends on what is measured. (B) Matter Matter as particles ⇒ obvious from everyday experience Matter as waves (deBroglie, 1929, Nobel Prize for his Ph.D. thesis!) Same relationship between momentum and wavelength for light and for matter p= h λ ⇒ λ= h p ≡ de Broglie wavelength Amazing notion! But wavelength only observable for microscopic momentum e- crystal lattice Diffraction pattern 5.61 Fall 2007 Lecture #5 page 4 Consequences (I) (1) on Bohr atom + + If e- wave does not close on itself, eventually destructive interference will kill it! If e- wave does close on itself, then constructive interference preserves it. Criterion for stability: nh nh = p mv nh or mvr = = n! 2π ⇒ " = n! 2π r = nλ = As Bohr had assumed angular momentum is quantized!