lecture10 - Physics 126 Lecture 10 Matter Wave Dawn before...

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M.Loy, H. B. Chan 1 Physics 126 Lecture 10 March 11 2011 Matter Wave: Dawn before the birth of Quantum Mechanics Reading: Chapter 3 of Text pentasterisk6 The two broad themes: (a) nature of radiation (b) nature of matter (atoms) pentasterisk6 de Broglie Matter Wave Hypothesis pentasterisk6 Davisson-Germer Electron Diffraction: Experimental verification of wave nature of matter pentasterisk6 Wave Properties pentasterisk6 Fourier Series pentasterisk6 Wave Packet pentasterisk6 Phase and Group velocity pentasterisk6 Uncertainty Principle pentasterisk6 Need for the development of a ‘new mechanics’
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H. B. Chan 2 Midterm exam boxshadowdwn March 26, Saturday, LTJ (TA’s will send out seating plan) pentasterisk6 2:30 to 5:00 pm boxshadowdwn Covers Lectures 1 – 12 boxshadowdwn Closed Book pentasterisk6 Complicated formulae and physical constants will be provided pentasterisk6 Fundamental Equations such as below will NOT be provided. pentasterisk6 Lorentz Transform pentasterisk6 E 2 = (pc) 2 + (mc 2 ) 2 , β β = pc/E pentasterisk6 Key Discoveries leading to the new Quantum Mechanics You are expected to know: pentasterisk6 How the experiment was done and what were the key observations pentasterisk6 What the experiment proved, or disproved pentasterisk6 In what ways are that experiment important You will not be tested on the date and the place of the experiments.
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M.Loy 2010 3 WAVE-PARTICLE DUALITY OF LIGHT “ There are therefore now two theories of light, both indispensable, and … without any logical connection.” Einstein 1924 Evidence for wave-nature of light • Diffraction and interference Evidence for particle-nature of light • Photoelectric effect • Compton effect We need both to explain what we observe experimentally.
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M.Loy, H. B. Chan 4 θ λ = 2dsin θ X-ray diffraction Wavelength < 1 nm Use crystals as the “grating” Compton scattering Shift in wavelength of scattered X-ray λ ’ – λ = (h/m e c)(1 - cos θ ).
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M.Loy 2010 5 We need the dual nature of light to understand the COMPTON SCATTERING experiment! X-ray source Target Crystal (selects wavelength) Collimator (selects angle) θ Result: peak in scattered X-ray radiation shifts to lower energy (longer wavelength) than source. Amount depends on θ (but not on the target material). Measurement of the energy of the scattered X-ray requires the scattered X-ray to be wave , and its wavelength satisfy E = hc/ λ Detector Compton With Bragg crystal spectrometer technique, X-ray sources with definite energy can be used for precise experiment. This requires X-ray to be wave to be diffracted by the spectrometer. Yet all these results only make sense when we treat X-ray as particles with energy E = h ν and momentum p = h/ λ .
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M.Loy 2010 6 boxshadowdwn Particle-Wave Duality: Bohr’s Principle of Complementarity boxshadowdwn If your experiment is designed to measure its particle property, it behaves as particle (the scattering of photon and electron in Compton Scattering); boxshadowdwn and if your experiment is designed to measure its wave
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