2010 PHYSICS 002C Lecture 23

2010 PHYSICS 002C Lecture 23 - PHYSICS 002C Lecture 23 May...

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PHYSICS 002C Lecture 23 May 22, 2009 Serway and Jewett Chapter 28 – Quantum Mechanics Old: Chap 28.1-3 Blackbody radiation, the photo & Compton effects proved beyond doubt that light comes in little packets of energy hf E and somehow is able to exhibit wave-like interference effects. Old: Chap 28.4,5 – Electron diffraction experiment of Davisson and Germer proves that electrons are able to exhibit wave-like interference effects, verifying de Broglie’s (1922) hypothesis - p h / . Wave-Particle duality New: Probability amplitudes, wave functions, tunneling and uncertainty Chap 28.6 – The quantum particle What is an electron? is answered by what we can measure about it. Internal properties: Charge -1.602 176 46 10 -19 C Mass 9.109 381 10 -31 kg “Radius” <10 -17 m Spin angular momentum 2 1 Magnetic moment -928.476 4 10 -26 JT -1 Lepton number +1 Compton wavelength 2.426 310 22 10 -12 m g-factor -2.002 319 304 374 External properties Position (x,y,z) Velocity Momentum Angular momentum Kinetic Energy We know we are observing an electron if we detect something with some of the stated internal properties, charge and mass being sufficient. Suppose an electron has been produced in a known state with momentum p . As long as the electron does not interact with anything after its production, all we know is p . Where might the electron be found if we measure x ? If we don’t measure is the electron at some particular point? No! x The first postulate of quantum mechanics is that the state of any quantum system (like an electron) is specified by a complex probability amplitude, the absolute square of which gives you the probability for measuring something. 1
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The picture of diffraction is the same whether you have a beam of photons or electrons. A probability amplitude describing a plane wave traveling in the x direction )} ( exp{ ) ( t kx i x passes through a grating and becomes a different probability amplitude wave as it nears the screen. When it interacts with the screen, the local phases of the original wave are hopelessly scrambled with the zillions of degrees of freedom of the screen (atomic vibrations, electron motions). Averaging over all these phases leaves us with only the probability 2 ) ( ) ( y y P SCREEN . After the interaction with the screen (i.e. the measurement) the different parts of the old electron wave function can no longer interfere with each other and the electron is definitely located somewhere. How do the other parts of the wave function know to vanish when you detect an electron? The situation is more startling in the following experiment. Measurement of Correlated variables and the Einstein-Padolsky-
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This note was uploaded on 09/23/2010 for the course PH 02c taught by Professor Mile during the Spring '04 term at Riverside Community College.

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2010 PHYSICS 002C Lecture 23 - PHYSICS 002C Lecture 23 May...

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