Lect10 - All of modern physics is governed by that...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
“All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics. ..It has survived all tests and there is no reason to believe that there is any flaw in it….We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.” --Murray Gell-Mann
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Barrier Penetration and Tunneling U(x) 0 x AB C B A nucleus x 0L U 0 x U(x) E
Background image of page 2
Overview Overview z How quantum particles tunnel z Nuclear Decay z Solar Fusion z NH 3 Maser
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
z Due to “barrier penetration”, the electron density of a metal actually extends outside the surface of the metal! Leaky” Particles: Revisited Leaky” Particles: Revisited 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 x = 0 x distance x outside the surface of the metal at which the electron probability density drops to 1/1000 of that just inside the metal. 1000 1 ) 0 ( ) ( 2 2 2 = Kx e x ψ nm K x 3 . 0 1000 1 ln 2 1 = () 1 0 22 2 5 2 2 11.5 1.505 ee mm eV KV E n m he V n m ππ =− = = = using
Background image of page 4
Application: Application: Tunneling Microscopy Tunneling Microscopy z Due to the quantum effect of “barrier penetration,” the electron density of a material extends beyond its surface: material STM tip STM tip material ~ 1 nm x Metal tip One can exploit this to measure the electron density on a material’s surface: Real STM tip STM images DNA Double Helix: www-aix.gsi.de/~bio http://www.quantum-physics.polytechnique.fr/en/ Na atoms on metal:
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
U(x) x I II III 0 L U=0 U=U o z Find Transmission Coefficient, “T” , the probability an incident particle tunnels through the barrier. The particle can be represented by a packet with a narrow range of k, coming in only from the left (positive k) Let’s look, for a single k, at how much transmitted density there is, compared to the incident density. Tunneling Through a Barrier (1) Tunneling Through a Barrier (1) Region I: 12 () ikx ikx I xA e A e ψ =+ E > U: oscillatory solution We solve for ψ in each of the three regions shown. in reflected Kx Kx II e B e B x + = 2 1 ) ( Region II: E < U: exponential solutions Region III: 1 ikx III xC e = E > U: oscillatory solution transmitted
Background image of page 6
Tunneling Through a Barrier (2) Tunneling Through a Barrier (2) z Next we would need to apply the “continuity conditions” for both ψ and d ψ /dx at the boundaries x = 0 and x = L to determine the A, B, and C coefficients. FOUR EQUATIONS. z A 1 doesn’t matter- it just sets the average intensity of the incoming wave, and what we’re after is just the fraction that goes through. Multiplying A 1 by a constant would just multiply everything by the same constant, and not affect ratios.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/15/2008 for the course PHYS 214 taught by Professor Debevec during the Spring '07 term at University of Illinois at Urbana–Champaign.

Page1 / 30

Lect10 - All of modern physics is governed by that...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online