Activity 24: Tunneling

In today's activity, you will use a shockwave routine to examine tunneling.

Before You Start:
Answer the following questions to the best of your ability before doing the experiment.

A good example of a potential barrier is a fence in someone's yard. A baseball that has gravitational potential greater than the height of the fence (so potential energy is greater than mgh, where h is the fence's height) will sail over. A baseball without enough gravitational potential will hit the fence and be reflected.

If the baseball's potential is less than the height of the fence, will it ever make it to the other side of the fence?
If the baseball's potential is greater than the height of the fence, will it ever be reflected?
An example of a potential barrer for an electron would be a region of highly negative electric potential (like the negative terminal of a battery or the p side of a p-n junction). If an electron's energy were less than the potential energy of the barrier, would you expect an electron to ever be able to make it to the other side of the barrier?
If an electron's energy were greater than the potential energy of the barrier, would you expect an electron to ever be reflected from the barrier?

After you have thought about your answers, compare notes with your group members. Does everyone have the same predictions, or are there differing opinions?

Quantum Wells

Go to the web site http://phys.educ.ksu.edu/vqm/html/qtunneling.html. You may need to download a Shockwave plugin to use this page.

1. Write down the default parameters from the simulation:
Barrier width: ________________________
Barrier height: ________________________
Particle energy: _______________________
Planck’s constant: _____________________
The default particle is an electron. Is the electron's energy greater than or less than the barrier height? What do your predictions say will happen to the electron in this case?

2. Click on the "probability density" tab to show a graph of |c(x)|². Click on the Redraw Graphs button, and sketch the resulting graphs for Potential Barrier and Probability Density.

3. A sinusoidal probability density means there are some interference effects occurring (for example, when a reflected wavefunction combines with the original wavefunction traveling the other direction). A constant probability density represents a "plane wave", or a completely unconstrained object (it has equal probability of being anywhere). Using these guidelines, does the probability density graph in the previous question indicate a probability of the electron being reflected? Does it indicate a probability of finding the electron on the far side of the barrier? How does this compare to what you predicted?

4. Halve the Barrier width and sketch the resulting probability density graph on your paper, using the same scale as before. How does the probability of finding the electron on the far side of the barrier change? Does this result make sense?

5. Halve the particle energy and sketch the resulting probability density graph on your paper, using the same scale as before. How does the probability of finding the electron on the far side of the barrier change? Does this result make sense?

6. Increase the Particle Energy so it is higher than the Barrier Height. Sketch the resulting probability density graph on your paper, using the same scale as before.

7. Does the probability density graph in the previous question indicate a probability of the electron being reflected? Does it indicate a probability of finding the electron on the far side of the barrier? How does this compare to what you predicted?

You will be asked to complete an evaluation of today's activity and lecture before the start of next class. This evaluation counts as a free 5% of each activity grade.

1.	Write down the default parameters from the simulation: Barrier width: ________________________ Barrier height: ________________________ Particle energy: _______________________ Planck’s constant: _____________________ The default particle is an electron. Is the electron's energy greater than or less than the barrier height? What do your predictions say will happen to the electron in this case?
2.	Click on the "probability density" tab to show a graph of \|c(x)\|². Click on the Redraw Graphs button, and sketch the resulting graphs for Potential Barrier and Probability Density.
3.	A sinusoidal probability density means there are some interference effects occurring (for example, when a reflected wavefunction combines with the original wavefunction traveling the other direction). A constant probability density represents a "plane wave", or a completely unconstrained object (it has equal probability of being anywhere). Using these guidelines, does the probability density graph in the previous question indicate a probability of the electron being reflected? Does it indicate a probability of finding the electron on the far side of the barrier? How does this compare to what you predicted?
4.	Halve the Barrier width and sketch the resulting probability density graph on your paper, using the same scale as before. How does the probability of finding the electron on the far side of the barrier change? Does this result make sense?
5.	Halve the particle energy and sketch the resulting probability density graph on your paper, using the same scale as before. How does the probability of finding the electron on the far side of the barrier change? Does this result make sense?
6.	Increase the Particle Energy so it is higher than the Barrier Height. Sketch the resulting probability density graph on your paper, using the same scale as before.
7.	Does the probability density graph in the previous question indicate a probability of the electron being reflected? Does it indicate a probability of finding the electron on the far side of the barrier? How does this compare to what you predicted?