The aim of this project is to give a clear and pedagogical presentation of a “problem” or “phenomenon” in quantum mechanics.

- A “problem” could be similar to but more elaborate than the type of problems that appear on problem sets. For example, squeezed states were introduced briefly in the context of the harmonic oscillator in
*8.05 Quantum Physics II*. A student might delve deeper into the squeezed state formalism, describe the properties of squeezed states, explain the types of problems where they are useful, and give some examples of their applications. Such a paper would resemble a short chapter in some hypothetical textbook for 8.05. The principal references for a paper like this could be existing quantum mechanics texts and the references to the original literature to be found in them. - A paper focused on a “phenomenon” would introduce the phenonomenon and explain its origins in terms of the concepts and language of 8.06. For example, in studying the properties of atoms, we will briefly mention phenomena such as line-width, Thomas precession, and the Lamb shift. To write a paper about atomic line-widths, for example, a student might find out what some of the dominant types of line broadening are, when and how one can reduce them, and might talk about experiments that have managed to do so. Once again the principal references would likely be texts, perhaps modern physics texts in this case, histories of quantum physics, and the original literature.

Papers on “problems” might be based at least in part on your own calculations. Papers on “phenomena” might involve some library research. In either case reference must be given for any material taken from other sources. Do not plagiarize. Anyone who contemplates borrowing material directly from mainstream texts should consider how difficult it is to find a text that presents quantum physics at the level appropriate to 8.06.

We encourage students to write papers which expand upon a problem or phenomenon which was already introduced in either 8.05 or 8.06 lectures. If you do this, you should begin at the level of whatever we have already covered and then go farther. Students may also choose topics which have not appeared at all in class, but whose quantum mechanical explanation can be understood based upon what we have learned in 8.05 and 8.06.

Please do not try to choose subjects which are obscure, difficult, or controversial. Misguided attempts like this to gain the respect of the faculty inevitably have the opposite effect. There are plenty of deep, interesting, and challenging subjects in the mainstream of quantum mechanics.

Papers can range between 3.5 and 7 pages in length (in the RevTeX final, two-column format) including references and figures. These limits are firm. Students are encouraged to use equations and figures to aid their presentation, much as they are used in articles and textbooks.

### Ingredients of a good term paper

Ideally, a term paper should contain some calculation and some context (historical, mathematical, physical, engineering, etc.). The sample paper on reflectionless potentials does a good job of showing what level of calculations is right: enough detail for an 8.06 student to follow, but not an excessive amount. However, there are a few ways that your own papers should differ. First, this paper shows more originality than you need to: it gives a solution to a problem that has not previously been published (even if it had been “folklore” before), which is not reasonable to ask of you. On the other hand, it would be better if it gave more of a connection to a real-world scenario. Given the topic, this would be difficult, but the discussion section still gives an idea of the type of material that is good to include.