1 / 12

Quantum Mechanics: Tunneling

Quantum Mechanics: Tunneling. Physics 123. Wave Function. (Wave function Y of matter wave) 2 dV =probability to find particle in volume dV . In 1-dimentional case probability P to find particle between x 1 and x 2 is

ebobby
Télécharger la présentation

Quantum Mechanics: Tunneling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Quantum Mechanics:Tunneling Physics 123 Lecture XVI

  2. Wave Function • (Wave function Y of matter wave)2dV=probability to find particle in volume dV . In 1-dimentional case probability P to find particle between x1 and x2 is • Unitarity condition (probability to find particle somewhere is one): • Schrödinger equation predicts wave function for a system • System is defined by potential energy, boundary conditions Lecture XVI

  3. Properties of Wave function • Wave function respects the symmetry of the system • For example if the system is symmetric around zero • x-x • then wave function is either symmetric or antisymmetric around zero: Lecture XVI

  4. Count knots 0 knots in the box symmetric 1 knot in the box antisymmetric 2 knots in the box Symmetric N-th state: (N-1) knots in the box N-odd – symmetric N-even - antisymmetric Lecture XVI

  5. Particle in a finite potential well U0 I II III x 0 L • Particle mass m in a finite potential well: • U(x)=0, if 0<x<L, • U(x)=U0, if x<0-or-x>L • Boundary conditions: Lecture XVI

  6. Particle in a finite potential well U0 I II III x 0 L • Inside the box (region II) • Possible solutions: sin(kx) and cos(kx) Lecture XVI

  7. Particle in a finite potential well U0 I II III x 0 L • Outside the box (regions I and III) • Possible solutions: exp(Gx) and exp(-Gx) Lecture XVI

  8. Wave functions 2 knots in the box Symmetric 1 knot in the box antisymmetric 0 knots in the box symmetric Lecture XVI

  9. Probability to find particle at x • Particle can be found outside the box!!! • E=U0+KE • KE must be positive • KE=E-U0, but U0>E • Energy not conserved?! • Fine print: Heisenberg uncertainty principle • Time spent outside the box is less than h/2p divided by energy misbalance, then energy non-conservation is “virtual”=undetectable Lecture XVI

  10. Probability to find particle at x Consider electron mc2=0.5 MeV with U0=2eV, E=1eV How much time does it spend outside the box? Characteristic depth of penetration x0: exp(-Gx)=exp(-x/x0) Lecture XVI

  11. You can go through the wall!!! • It’s called tunneling effect • Probability of tunneling P=|y|2=exp(-2GL), L-width of the barrier • Transmission coefficient T~P=exp(-2GL) Lecture XVI

  12. Problem 39-34 • A 1.0 mA current of 1.0 MeV protons strike 2.0 MeV high barrier of 2.0x10-13m thick. Estimate the current beyond the barrier. p Lecture XVI

More Related