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Quantum Tunneling

Quantum Tunneling. Free Wave Packet Tunneling through a Barrier Tunneling over a Well Example: Tunneling Microscope Tunnel Transistor a -particle decay. Quantum Tunneling. Postulates Maybe in lab. Quantum Tunneling. Time Dependent Wave Equation.

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Quantum Tunneling

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  1. Quantum Tunneling Free Wave Packet Tunneling through a Barrier Tunneling over a Well Example: Tunneling Microscope Tunnel Transistor a-particle decay

  2. Quantum Tunneling Postulates Maybe in lab

  3. Quantum Tunneling Time Dependent Wave Equation What is the assumption Junior?

  4. Quantum Tunneling Free Wave Packet in One Dimension For one-dimension we have Recall we make up a wave packet using Fourier analysis.

  5. E E Quantum Tunneling Potential Step Barrier The energy can be greater or less than the potential barrier. E > U0 E < U0

  6. Lets first try to guess the wavefunction! Quantum Tunneling Potential Step Barrier First we will consider E < U0 Region I U(x)=0 Region II U(x)=U0 Boundary Conditions

  7. but Quantum Tunneling E < U0 Potential Step Barrier Reflection Coefficient Transmission Coefficient

  8. Lets first try to guess the wavefunction! Quantum Tunneling Potential Step Barrier Next we will consider E > U0 Region I U(x) = 0 Region II U(x) = U0 Boundary Conditions

  9. Quantum Tunneling E < U0 Potential Step Barrier Reflection Coefficient Transmission Coefficient

  10. Lets first try to guess the wavefunction! Quantum Tunneling Potential Barrier for E < U0 Region I U(x) = 0 Region II U(x) = U0 Boundary Conditions Region III U(x) = 0

  11. Quantum Tunneling Potential Barrier E < U0 Solving these four equations you find

  12. Quantum Tunneling Wave Packet Impinging on A Step Simulations For E > U0 http://phet.colorado.edu/new/simulations/sims.php?sim=Quantum_Tunneling_and_Wave_Packets

  13. Quantum Tunneling Tunneling Microscope

  14. Quantum Tunneling Tunneling Microscope

  15. Quantum Tunneling a-particle Decay

  16. Quantum Tunneling Ammonia NH3 MASER

  17. Quantum Tunneling Quantum Tunneling (Esaki) Diode A tunnel diode or Esaki diode is a type of semiconductor diode which is capable of very fast operation, well into the microwave frequency region, by using quantum mechanical effects.

  18. Quantum Tunneling Quantum Tunneling Transistor Will replace MOPSET’s ECE Headline News High-speed signal mixer demonstrates capabilities of transistor laser By James E. Kloeppel, U of I News BureauMarch 26, 2009 Single electron transistor (SET)

  19. Quantum Tunneling Scattering: Potential Well E > U0 50 eV Lets guess the wavefunction! Lets look at the simulation. Is this a homework problem?

  20. Quantum Tunneling Next time….. What if the potential is ? …. called the finite square well.

  21. Quantum Tunneling Simulations A great Java tunneling simulation http://phet.colorado.edu/new/simulations/sims.php?sim=Quantum_Tunneling_and_Wave_Packets Have file phet tunneling???? Also has good tunneling simulations http://www.cs.unm.edu/~dstrain/sem/results.html http://phys.educ.ksu.edu/vqm/html/qtunneling.html

  22. Quantum Tunneling Something

  23. Quantum Tunneling Something

  24. P2(As2) TMIn 50nm 0.6 eV Ec InP InP InAs InAs InAs Quantum Tunneling Growth via Chemical Beam Epitaxy (CBE) A contacted InAs/InP nanowire Quantum Dots: Harvard Wire Research InAs/InP Heterostructured Nanowires Energy landscape TEM photo of InAs/InP nanowire

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