**Meeting time:** MWF 12:30–1:20

**Instructor:** Daniel V. Schroeder

**Office hours:** MWF 11:30–12:00 and Mondays 1:30–2:20. I will also be available later on
most MWF afternoons, and I can come in early MWF mornings if you make an appointment. I will not
be on campus most Tuesdays and Thursdays.

**Office:** SL 208

**Phone:** 801-626-6048 (note that I check email much more often than voicemail)

**Email:** dschroeder at weber dot edu

**Course web site:** http://physics.weber.edu/schroeder/quantum/

**Text:** I will hand out reading materials (and post them on the course web site) for much of
the semester. I also recommend that you obtain and use a standard undergraduate quantum
mechanics textbook such as David J. Griffiths, *Introduction to Quantum Mechanics*, second edition
(Pearson Prentice Hall, 2005).

There are many practical reasons to study quantum mechanics, since it underlies and illuminates so many aspects of physics, chemistry, and modern technology. Furthermore, the mathematical tools of quantum mechanics (calculus, linear algebra, Fourier analysis) are used in a much wider array of scientific disciplines. More generally, studying quantum mechanics will continue to build your skills in problem solving and quantitative reasoning.

On a less practical level, many students are simply curious about quantum mechanics, since it makes such outrageous assaults on our common ways of thinking about the world. Personally, I also find it highly satisfying to “understand” nature at the deepest possible level. But perhaps most importantly, quantum mechanics forces us to think in new, unfamiliar ways: to develop intuition for the counter-intuitive. It is this kind of experience that constitutes education in the truest sense. Thus I hope you will find your study of quantum mechanics to be not merely informative, but also liberating.

This course will treat the theory of quantum mechanics at a more advanced level than you saw in
your Introductory Modern Physics (2710) course. While this is mostly a course in quantum *theory*,
I will also try to introduce some applications as time allows. The course will be divided into four
major sections:

**Wave mechanics in one dimension.**We will begin with the quantum mechanics of a single, structureless particle moving in one dimension. In this restricted and reasonably familiar context, we will work to obtain a general understanding of wavefunctions, quantum uncertainties, and energy quantization. We will use one-dimensional model systems to understand trapped particles, vibrating molecules, electrons in molecules and solids, and tunneling.**The general theory of quantum mechanics.**Next we will generalize quantum theory to include particles moving in more than one dimension, systems of more than one particle, and particles with internal structure. The new concept of*entanglement*arises in all of these more complicated systems. To encompass these systems we will use the powerful mathematical language of vector spaces, linear operators, and eigenvectors, and eigenvalues.**Three-dimensional systems.**We continue with an in-depth look at the quantum mechanics of a single particle in three dimensions, emphasizing the special case of spherically symmetric systems in which angular momentum is conserved. The most important (but not the only) application will be to a particle trapped in a Coulomb potential, that is, the hydrogen atom.**Spins and quantum information.**Finally we turn to mathematically simpler (but more abstract) systems in which it is the internal structure (usually spin or polarization) that is of primary interest. Besides the traditional applications to atomic physics, we will use this context to explore entanglement in some depth, as illustrated by Bell’s theorem, quantum cryptography, and quantum computing.

As mentioned above, I will try to hand out **reading materials** throughout most of the semester.
I will expect you to read these handouts before coming to class, and to participate in class
discussions. At this point in your education it is no longer acceptable to just sit back and listen.

I am not planning on doing a lot of lecturing. Instead we will spend **class time** on questions,
examples, activities, and discussion.

We will have 12 **problem sets**. As usual in a theoretical physics course, this is
where most of the learning will take place. The problem sets are not tests, and you are not expected
to be able to solve every problem correctly the first time, on your own. On the other hand, you
won’t learn anything if you rely on others too heavily as you work the problems. So here are the
rules:

- Spend at least ten minutes on each problem (or part thereof), making a good-faith effort to solve it yourself, before you seek help on it from anyone else.
*Do*ask me or a classmate for a hint if you are still stuck on a problem after 10 or 15 minutes. You may also ask for hints from other WSU faculty members. When asking for a hint, it’s usually helpful if you first explain what you do already understand.- When you obtain assistance from someone, acknowledge that person by name in your writeup of the problem. Be specific about exactly how that person helped: “Special thanks to L. Meitner for reminding me that neutrons are fermions.” Please don’t feel embarrassed for having obtained help. This is absolutely routine in academia, but we always acknowledge the assistance we receive.
- Whether or not you obtain assistance in solving a problem, be sure to check your answers with classmates or with me. If this check results in a revision to your solution, include an acknowledgment as described above.
- Never look at anyone else’s written solution before turning in your own. This includes
any and all solutions written by me or by other instructors or students or anyone else. Do not tempt
your classmates by showing them your own written solutions. Comparing
*answers*(including intermediate results) is encouraged but comparing entire*solutions*is not allowed. - Never seek help from internet sites, or from anyone not affiliated with WSU, without advance permission.
- Naturally, you may consult any source you like
*after*you have turned in your own solutions. - If you are ever in doubt about the interpretation of these policies, ask.

Take pride in your work! Your final written solutions to problem sets should be clearly presented and fully explained, at a level of detail that any of your classmates could read and understand. While your solutions needn’t be of publication quality, they should be reasonably legible and well organized.

Problem sets must be submitted on paper, not electronically. Please leave room in the margins for my comments.

Late problem sets will be marked down by 1/3 of the total credit for each day or partial day. However, only your 11 highest problem set scores (out of 12 total) will count toward your final grade, so you may miss one problem set without penalty. This policy should provide enough flexibility to accomodate most illnesses, family emergencies, unexpected romances, and the like. In the case of extended illness or other long-term emergency, please consult with me at the earliest opportunity.

We will have three closed-book **midterm exams**, each with a time limit of 90 minutes,
given in the Science Testing Center. You will have a 47-hour window (minus those
hours when the testing center is closed) in which to
take each exam.

At the end of the course you will complete a **final project** that will be based on an
article of your choice from the American
Journal of Physics or a similar journal. In brief, you
will choose an article on a topic in quantum mechanics that interests you, reproduce the
calculations (or a substantial portion of them, perhaps with some modifications) in the article, and then explain the article to
your peers
in a 15-minute presentation and in a formal paper (written up as a “note”
commenting on the original article). Not all articles are suitable for this assignment
so please obtain my approval of your choice before you begin any significant work.
Also please consult with me regarding the type of outside help that
might be appropriate as you
carry out your project work; in all cases you must explicitly give credit to each
source that you relied upon, explaining how you relied upon it. The presentations will take
place during our scheduled final exam time: Wednesday, April 27, 1:00 to 2:50 pm.

I will calculate your final grades using the following percentage weights:

Problem sets (11 @3%) | 33% |

Midterm exams (3 @15%) | 45% |

Class participation | 8% |

Final project | 14% |

In the event of a snow day or other campus shutdown, please check your email as soon as you can for specific instructions regarding this course. Obviously I will not require you to turn in a problem set or take a test on a day when the campus is closed, but otherwise you should assume that all deadlines are still in effect unless I explicitly modify them. It is your responsibility to make sure I have your correct email address.

Any student requiring accommodations or services due to a disability must contact Services for Students with Disabilities (SSD) in room 181 of the Student Service Center. SSD can also arrange to provide course materials (including this syllabus) in alternative formats if necessary.

Academic dishonesty, though rare, occasionally does occur in physics classes, so the following policies are necessary. Inappropriate collaboration or other dishonesty on homework will result in a zero grade for that problem set on the first occurrence and failure in the course thereafter. Dishonesty of any sort on a test or final project will result in automatic failure in the course. In serious cases, evidence of dishonesty may also be presented to the appropriate hearing committee for possible further sanctions.