Lect14 - Le cture14: Barrie Pe tration and Tunne r ne ling...

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Lecture 14, p 1 Lecture 14: Barrier Penetration and Tunneling x 0 L U 0 x U(x) E U(x) 0 x A B C B A nucleus
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Lecture 14, p 2 Today Tunneling of quantum particles Scanning Tunneling Microscope (STM) Nuclear Decay Solar Fusion The rest of the course: Next week : 3 dimensions - orbital and spin angular momentum H atom, exclusion principle, periodic table Last week : Molecules and solids. Metals, insulators, semiconductors, superconductors, lasers, . . Good web site for animations http://www.falstad.com/qm1d/
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Lecture 14, p 3 Due to “barrier penetration”, the electron density of a metal actually extends outside the surface of the metal! E F Occupied levels Work function Φ V o Assume that the work function (i.e., the energy difference between the most energetic conduction electrons and the potential barrier at the surface) of a certain metal is Φ = 5 eV . Estimate the distance x outside the surface of the metal at which the electron probability density drops to 1/1000 of that just inside the metal. 2 2 2 ( ) 1 1000 (0) Kx x e ψ - = x = 0 x 1 1 ln 0.3 2 1000 x nm K   = - ≈     “Leaky” Particles: Revisited ( 29 -1 0 2 2 2 2 2 5 2 2 11.5 nm 1.505 eV nm e e m m eV K V E h π = - = Φ = = h
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Lecture 14, p 4
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Tunneling: Key Points In quantum mechanics a particle can penetrate into a barrier where it would be classically forbidden. The finite square well: In region III, E < U 0 , and ψ (x) has the exponential form D 1 e -Kx . We did not solve the equations – too hard! You did it using the computer in Lab #3. The probability of finding the particle in the barrier region decreases as e -2Kx . The finite-width barrier: Today we consider a related problem – a particle approaching a finite-width barrier and “tunneling” through to the other side. The result is very similar, and again the problem is too hard to solve exactly here: The probability of the particle tunneling through a finite width barrier is approximately proportional to e -2KL where L is the width of the barrier. U(x)
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This note was uploaded on 02/21/2011 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect14 - Le cture14: Barrie Pe tration and Tunne r ne ling...

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