8B - 19 Quant At_11.ppt - Wave Mechanics Methods in Quantum...

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Wave Mechanics Methods in Quantum Theory More Generalities & Atoms
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General Properties 0f Waves Energy Momentum Pressure Polarization Reflection Refraction Diffraction Interference Localization by superposition of various wavelengths Total Internal Reflection - Frustrated (Tunnel) Standing waves (modes of vibration)
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Tunneling of waves Tunneling - Waves can leak out into spaces that are forbidden: Light waves in “total” internal reflection. (Frustrated total internal reflection, FTIR) Electrons into regions where they are have not enough energy. (Tunneling)
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‘Frustrated’ Total Internal Reflection A 45 Ň -90 Ň prism will deflect a beam of light by total internal reflection. When two such prisms are sandwiched back-to-back and pressed together, the air-glass interface can be made to vanish and the beam then propagates onward undisturbed. This transition, from total to no reflection, occurs gradually as the air film is made to thin out by progressively squeezing the prisms together harder until they make intimate contact. Optically speaking, if the evanescent wave extends with appreciable amplitude across the rare medium (air) into a nearby medium of higher refractive index (the 2nd prism), energy may flow across the gap (FTIR). FTIR is an optical analog of a quantum mechanical phenomenon called “tunneling”.
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Demo - “tunneling” of microwaves Total internal reflection can be “frustrated” by bringing another medium within about a wavelength.
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Tunneling Applications Radioactive decay - “ α - particles” bound within nuclei can escape through high potential barriers. (Gamow, 1928) Electrons tunnel at electrodes into ionic solutions. (Gurney, 1932) S canning T unneling M icroscope (STM) Moves a metallic tip within a few atoms- distance of a conductive surface to measure topgraphy of the surface. (Binnig & Rohrer , 1981)
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Original Paper on radioactive decay Radioactivity explained by tunneling - G. Gamow Z. fur Physik, 51 , 204 (1928)
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Scanning tunneling microscope A sharp tip. In fact, because of the exponential decrease of current with distance into the gap, it is the last atom at the end through which current mostly flows; and Nature usually provides a last atom so it is not as difficult as it looks. (Take that, Murphy’s Law.) Binnig & Rohrer, 1981
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STM operation Feedback (vertical control) currents are sent to adjust the gap between the tip and surface in order to keep the tunnel-current constant. The feedback current, proportional to the vertical height profile, is plotted as the tip is scanned left/right. Wavefunction amplitude
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STM image of graphite surface Graphite can be scanned in air. (HOPG = Highly oriented pyrolytic graphite)
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General Properties 0f Waves Energy Momentum Pressure Polarization Reflection Refraction Diffraction Interference Total Internal Reflection - Frustrated (Tunnel) Standing waves (modes of vibration)
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Chladni modes Sound vibrations in restricted geometries give shorter wavelength, more varied patterns as the frequency increases. Some videos: Square plate: http: //rogerbourland .com/blog/2006/05/30/chladni-patterns-video/ http://www.youtube.com/watch?v=Sz1AuS-qA1c&feature=related
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This note was uploaded on 05/02/2011 for the course PHYS 8B taught by Professor Catherinebordel during the Spring '10 term at University of California, Berkeley.

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8B - 19 Quant At_11.ppt - Wave Mechanics Methods in Quantum...

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