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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 ℓ 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 ℓ Spherical harmonics Selection rules Walking through walls • When E < U , wavefunction ψ dies off to 1 / e of its amplitude in a distance δ of 1 /α , or δ = 1 α = planckover2pi1 radicalbig 2 m ( U − E ) (1) • The probability ∝ ψ 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 δ/ 2. • But perhaps nucleons can escape from the nucleus by tunneling! George Gamow, 1936: explanation for radioactivity. We’ll get to this . . . • Tunneling of an electron over a 5 eV gap: x t = planckover2pi1 2 radicalbig 2 m ( V − E ) = 1 2 π hc 2 radicalbig 2 mc 2 ( V − E ) = 1 2 π 1240 eV · nm 2 √ 2 · 511 × 10 3 eV · 5 eV = . 044 nm so for every 0.1 nm or 1 Å 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 ℓ 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 Rohrer’s third STM: Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and ℓ 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 ℓ 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 ℓ Spherical harmonics Selection rules The Quantum Corral Don Eigler’s quantum corral : Finite square well Tunneling Scanning tunneling microscope Heisenberg uncertainty Expectation values The atom Spherical coordinates Radial wavefunctions n and ℓ Spherical harmonics Selection rules Diffraction from a slit You’ve probably seen this construction in your first...
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 Fall '01
 Rijssenbeek
 Physics, Heisenberg, Heisenberg uncertainty Expectation, microscope Heisenberg uncertainty, Spherical harmonics Selection, harmonics Selection rules

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