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Unformatted text preview: Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules Finite square well (Serway 6.5) Region II: particle free to travel. Regions I and III: classically forbidden. x =0 x = L U =0 U = U I II III Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules Walking through walls When E < U , wavefunction dies off to 1 / e of its amplitude in a distance of 1 / , or = 1 = planckover2pi1 radicalbig 2 m ( U E ) (1) The probability 2 will be attenuated by exp [ 1 ] = exp [ 1 / 2 ] 2 = e ( 1 2 ) 2 = . 37 when we have traveled a tunneling distance x t of / 2. But perhaps nucleons can escape from the nucleus by tunneling! George Gamow, 1936: explanation for radioactivity. Well get to this . . . Tunneling of an electron over a 5 eV gap: x t = planckover2pi1 2 radicalbig 2 m ( V E ) = 1 2 hc 2 radicalbig 2 mc 2 ( V E ) = 1 2 1240 eV nm 2 2 511 10 3 eV 5 eV = . 044 nm so for every 0.1 nm or 1 the current will be reduced by a factor of exp [ . 1 / . 044 ] = . 1. Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules The scanning tunneling microscope The first STM, with its inventors Heinrich Rohrer (b. 1933) and Gerd Binnig (b. 1947) at the IBM Zurich lab (they won the 1986 Nobel Prize): Binning and Rohrers third STM: Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules Modern STMs Veeco Instruments: an exam ple of a system that can be run on a desk top. RHK Instruments: an exam ple of an ultra high vacuum system for surface studies. Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules Example STM images Silicon (111) surface, 7 7 reconstruction. Courtesy RHK Instruments. Iron monolayer making FeSi on Si (111). Courtesy RHK instruments. Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules The Quantum Corral Don Eiglers quantum corral : Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and Spherical harmonics Selection rules Diffraction from a slit Youve probably seen this construction in your first...
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This note was uploaded on 05/28/2011 for the course PHY 251 taught by Professor Rijssenbeek during the Fall '01 term at SUNY Stony Brook.
 Fall '01
 Rijssenbeek
 Physics

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