About the Course & Materials
We have compiled information about the course as we have taught it. You will find information on the text, ordering of topics, course expectations, as well as a description of the transformed materials and their use.
Quantum Mechanics and Atomic Physics 1, is the first semester of our two-semester sequence of quantum mechanics. Topics include the Schrödinger equation, wave functions, probability, the uncertainty principle, stationary states, the infinite square well, the harmonic oscillator, Hilbert space and formal operator methods, three dimensional systems including the hydrogen atom, and, spin and angular momentum.
The primary text for this course is D.J. Griffiths “Introduction to Quantum Mechanics" 2nd Edition (Prentice Hall, New Jersey, 2005).
The next are all very much at Griffiths' level (and have been used or considered as primary texts in the past)
- S. Gasiorowicz: "Quantum Physics"
- R. Liboff: "Introductory Quantum Mechanics"
- R. Robinett: "Quantum Mechanics"
- R. Scherrer: "Quantum Mechanics"
Other books of possible use for this course:
- Feynman, Leighton, and Sands: "The Feynman Lectures on Physics, part III." (Part of a truly wonderful series of 3 "introductory" physics books.)
- M. Boas: "Mathematical Methods in the Physical Sciences" (very useful for mathematical tricks and techniques you may have forgotten)
The following additional textbooks were recommended by electrodynamics instructors at CU Boulder, and various physics faculty at outside institutions:
- P. Tipler: "Modern Physics" (slightly simpler level)
- Eisberg and Resnick: "Quantum Physics" (again slightly simpler level, although they cover lots of interesting and often advanced examples)
Course Topics & Ordering
The bulk of the material in this course is fairly canonical across universities. Following are some discussions on the presentation of particular topics and where they might appear in the course.
Additional commentary on the presentation of certain topics can be found in the Course Users Guide.
There are many mathematical prerequisites for this course, and students have varying degrees of comfort with this material. (See Learning Goals for detailed lists of prerequisites). Faculty may give a mathematical pre-test to students to both (a) assess where students are weak, and (b) send students the message that this is material they should already be familiar with.
There is a general consensus among faculty that the bulk of the learning in this course comes from doing the homework. This course is where students learn a certain level of sophistication in solving problems (see Learning Goals) and so assigned homework should reflect that higher expectation. We have compiled a homework bank of useful problems designed to target these higher level goals.
Additional ideas for creating homework sets can be found in the Course Users Guide.
There are a variety of lecture techniques that have been shown to be useful in student engagement.
1. Clicker questions
Clickers are wireless personal response systems that can be used in a classroom to anonymously and rapidly collect an answer to a question (usually multiple-choice) from every student. This allows rapid reliable feedback to both the instructor and the students. Alternatively, clicker questions can still be used without the personal response system by using colored cards or hand signals. See the Colorado Science Education Initiative website for additional information and resources for effective use of clicker questions.
Many of the more simple, conceptual homework problems can be reworked into clicker questions, serving two purposes: (a) students engage in meaningful discussion about the concept rather than seeking the answer, and (b) leaving more time for longer problems on the homework set. Faculty members, in conjunction with Science Teaching Fellows, have developed a bank of clicker questions. Clicker questions have proven very effective, though time consuming, in this course, generating a good deal of student discussion and highlighting student difficulties. In addition, because students’ knowledge is tested often, it is easier for them to know where their difficulties lie. One student remarked that the clicker questions in this class worked better than in other classes because they were integrated deeply into the lecture – they acted to connect one topic to the next, instead of a 5-minute aside. They were a bridge rather than a break in lecture.
We have compiled a Clicker bank containing concept test questions developed by faculty at CU and other institutions.
2. Interactive lecture
When solving a problem on the board, the lecturer can pause and ask the class for the next step. If the course culture has included the use of clicker questions, so that students are habituated to actually engaging with this sort of question (instead of waiting for the smartest student to answer), then this type of discussion can occur without the use of actual clickers in every instance. The class should be given a time limit (e.g., “You have 30 seconds, write down your answer”) to focus their discussion. For example, solving for the operator method of generating the spherical harmonics, the instructor might ask students to evaluate various commutators needed instead of just giving or deriving them for the students.
3. Class discussions
In addition to clicker questions, faculty can pose open-ended questions (non multiple choice) for discussion, providing students an opportunity to engage with the concepts in class. The more that instructors are clearly open to discussion in class, the more students will feel comfortable posing spontaneous questions.
4. Whiteboard or Chalkboard Activities
We have successfully used whiteboards and student work at the blackboard in class and out of class. Large (2x3 foot) whiteboards provide a convenient public work space for group activities. Small (1x1 foot) whiteboards work well for individual or partner work while still allowing instructor to quickly see what students are getting in a lecture (by walking around to individual whiteboards or by asking students to “publish” their results by holding up their whiteboards).
5. Don’t repeat examples from the text
Students generally read the chapter as they work on the problem set. It may be useful to encourage students to read the chapter before lecture, if the professor does not intend to reiterate material from the book in lecture. In that case, lecture may be spent in productive discussion and engagement with the material. Students can easily read derivations and similar content in the book, and so professors may decide how much of that content should be included in lecture.
While recitations can’t be mandatory for this 3-credit course at CU, it is useful to offer an instructor- or TA-led session to work on issues in the homework. In the reformed course, we encouraged students to work in small groups on the homework. They learn by peer instruction with occasional input from the instructor, as in the tutorials. Each group has a group-sized whiteboard (see above), and problems are not worked out on the board by the TA, as has been traditionally the case. We have offered two homework help sessions – two nights and one night before the homework is due.