Quantum Tunneling

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Quantum Tunneling

• Free Wave Packet
• Tunneling through a Barrier
• Tunneling over a Well
• Example Tunneling Microscope
• Tunnel Transistor
• a-particle decay

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Quantum Tunneling
Postulates Maybe in lab
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Quantum Tunneling
Time Dependent Wave Equation
What is the assumption Junior?
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Quantum Tunneling
Free Wave Packet in One Dimension
For one-dimension we have
Recall we make up a wave packet using Fourier
analysis.
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Quantum Tunneling
Potential Step Barrier
The energy can be greater or less than the
potential barrier.
E gt U0
E lt U0
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Quantum Tunneling
Potential Step Barrier
First we will consider E lt U0
Region I U(x)0
Region II U(x)U0
Boundary Conditions
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Quantum Tunneling
E lt U0
Potential Step Barrier
Reflection Coefficient
Transmission Coefficient
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Quantum Tunneling
Potential Step Barrier
Next we will consider E gt U0
Region I U(x) 0
Region II U(x) U0
Boundary Conditions
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Quantum Tunneling
E lt U0
Potential Step Barrier
Reflection Coefficient
Transmission Coefficient
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Quantum Tunneling
Potential Barrier for E lt U0
Region I U(x) 0
Region II U(x) U0
Boundary Conditions
Region III U(x) 0
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Quantum Tunneling
Potential Barrier E lt U0
Solving these four equations
you find
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Quantum Tunneling
Wave Packet Impinging on A Step
Simulations
For E gt U0
http//phet.colorado.edu/new/simulations/sims.php?
simQuantum_Tunneling_and_Wave_Packets
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Quantum Tunneling
Tunneling Microscope
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Quantum Tunneling
Tunneling Microscope
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Quantum Tunneling
a-particle Decay
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Quantum Tunneling
Ammonia NH3 MASER
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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.
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Quantum Tunneling
Quantum Tunneling Transistor
Will replace MOPSETs
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)
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Quantum Tunneling
Scattering Potential Well E gt U0
50 eV
Lets guess the wavefunction!
Lets look at the simulation.
Is this a homework problem?
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Quantum Tunneling
Next time..
What if the potential is ?
. called the finite square well.
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Quantum Tunneling
Simulations for you play with!
A great Java tunneling simulation
http//phet.colorado.edu/new/simulations/sims.php?
simQuantum_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