The final project provides you with an opportunity
to investigate some quantum mechanical systems of particular interest to you.
The project involves selecting an interesting area of quantum mechanics, and
writing a short paper that describes how to use quantum physics to understand a
particular physical effect, device, or process.
To keep things focused, I am suggesting four general
project areas. I strongly encourage you to select one of these project areas.
However, if you have a burning desire to study a different topic, I will
consider alternative proposals.
Regardless of topic area, the project involves two
pieces
Imagine writing your paper, not for me, but for someone else in the class. Even better, I'd recommend that you imagine addressing your paper to Yourself, but with your state of knowledge reset to where it was at the beginning of the course. In other words, hit the high points about the quantum mechanics that you need to understand the topic, and help the reader to actually understand how quantum physics explains what is happening. You don't need to produce elegant new derivations. Instead, try to provide a clean description of something that interests you. I particularly like papers that explain interesting problems that could be used for long homeworks!
An outline of your proposed paper is due on Monday, December 2. The outline is 25% of the project grade. The outline should include:
· A paragraph describing your topic, what you are particularly interested in explaining, and what particular part/parts of the course (special relativistic dynamics, 3-D Schrodinger Equation, etc.) you expect to be the most important foundation for your paper. (15 points)
· An outline of the major sections of the paper. (5 points)
· At least two references (books, articles, websites, or other published material) that you expect to use in your paper. (5 points)
I will read these paragraphs and outlines; I will return comments to you be Wed. Dec. 4 either approving the topic, or providing guidance, particularly for too ambitious projects.
Your paper should be 10-15 pages in length and will be worth 75% of the project grade. The paper must be formatted using some type of word processor. I will not be grading handwritten papers. In addition, papers should include the following:
· A title page with: 1) Title 2) Author 3) An abstract of no more than 300 words that describes the major points in your paper and what you have found. Think of this abstract as a concise description that you could recite to an interested reader to help them decide whether the paper is something that they’d like to read. (10 points)
· Your original graphs (if any) should include the code used to plot them e.g., Mathematica commands, and either the graphed function or a table of plotted data points. Figures taken from other sources must be referenced in the figure caption. Other technical graphs should be clear enough to allow an interested reader to reproduce the plots themselves (15 points)
· A references section with at least five references, including at least one of each of the following: Books, journal or technical articles, websites, popular magazine articles. You should include appropriate citations to these sources in your text. (25 points)
The finished papers will be submitted online (more details later) and a hard copy will be handed in to me by Monday, December 16, 2002.
1. Lasers
Lasers are at the heart of fiber optic
communication, home entertainment systems (DVD and CD-ROM), promise incredibly
dense holographic data storage systems, and so on. They are everywhere even
though the first laser was only invented 40 years ago (seems recent to me!).
Project Suggestions: Pick a particular type of
laser (diode, gas, solid state, etc.) and explain how the thing actually works,
where it is used, etc. The book explains the ruby solid state laser and the
He-Ne gas laser in some detail, so don't pick them.
Useful reading: Section 15.7 and 15.8
2. Superconductivity
Most of the time, we think of quantum mechanics as
providing us with the wave function of some very small object (say an electron
in a hydrogen atom). However, in superconductors, a huge number of the
electrons work together to fall into one huge quantum mechanical wave function.
The end result is a set of spectacular behaviors such as zero electrical
resistance, the ability to quantize magnetic flux in superconducting rings, the
ac Josephson effect, where the time dependence of the wave function becomes
directly measurable. Superconductors are the original 'macroscopic quantum
system'.
Project Suggestions: Describe the use of
superconductors in high field electromagnets for whole-body MRI imaging
(overlap with NMR below) or describe the NIST 'Josephson Voltage Standard'.
Useful reading: Section 17.8
3. Nuclear Magnetic Resonance/ Medical imaging
Two-level spin systems are the basis of many
interesting experimental techniques. Nuclear magnetic resonance has become one
of the most important laboratory techniques for chemical identification. It is
evolving into a major technique for measuring the structure of biological
molecules. Magnetic Resonance Imaging (MRI get rid of the 'nuclear' because
it's scary) is one of the most important medical imaging techniques since the
discovery of x-rays.
Project Suggestions: Explain how the quantum
spin of nuclei is measured in NMR and then explain how the technique can be
used to produce medical images. Perhaps describe '2-D NMR' and how it is used
to determine the structure of molecules.
Useful reading: Tipler and Llewellyn, Section 12-3.
4. Semiconductor Devices
If you want to understand the behavior of modern
electronics, especially integrated circuits, you need to understand some
quantum mechanics. Until quantum mechanics, even the basic issues in the
behavior of metals, insulators, and semiconductors (like why they are even stable
against collapse into the nucleus) could not be understood.
Project Suggestions: Pick an electronic device,
like the silicon field effect transistor, the photo diode, or perhaps the diode
laser (some overlap with the lasers project)
Useful reading: Chapter 17, sec 17.6.
5. Scanning tunneling microscopy
The scanning tunneling microscope allows us to look
at individual atoms and molecules on surfaces, by using quantum mechanical
tunneling. These microscopes, along with a host of related techniques like atomic
force microscopy, have revolutionized the study of surfaces.
Project Suggestions: Explain the tunneling
microscope and give an example of understanding the images from some
particularly interesting molecule or surface.
Useful reading: T&L Section 6-6 and the
whfreeman.com/physics website.
1. Relativity and quantum mechanics
Learn something about the Klein-Gordon or Dirac
equations (first efforts to produce something like the Schrodinger equation,
but consistent with special relativity).
Project Suggestions: Perhaps make some progress
on why one or another of these equations might be a reasonable guess to replace
the Schrodinger equation, and why they don’t work very well.
Useful reading: It’s a problem.
2. Relativistic dynamics
Use the modified Newton’s 2nd Law to
describe the motion of something fast. Perhaps work through a relativistic
space trip that seems interesting…
Project Suggestions: How about the feasibility
of traveling to the galactic core and back...
Useful reading: It’s a problem.
3. General Relativity
Many topics in this area, but it’s hard to keep
things on our level.
Project Suggestions: Maybe work more with the
Wilma problem, to show how light is bent by the gravitational field
Useful reading: It’s a problem.