# Lect14 - Lecture 14: Barrier Penetration and Tunneling...

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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 Ammonia Maser 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/
Lecture 14, p 3 “Leaky” Particles: Revisited 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 U o 2 ( ) 1 2 2 1000 (0) x Kx e ψ - = x = 0 x 1 1 ln 0.33 nm 2 1000 x K = - ( 29 -1 0 2 2 2 2 2 4.1 eV 2 2 10.4 nm 1.505 eV nm e m m K U E h π = - = Φ = = That’s small (about the size of an atom) but not negligible. The work function (the energy difference between the most energetic conduction electrons and the potential barrier at the surface) of aluminum is Φ = 4.1 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.

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Lecture 14, p 4
Lecture 14, p 5 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) U 0 I II III 0 L x

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Lecture 14, p 6 U(x) x I II III 0 L 0 U o What is the the probability that an incident particle tunnels through the barrier?
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## This note was uploaded on 01/19/2012 for the course PHYS 214 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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Lect14 - Lecture 14: Barrier Penetration and Tunneling...

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