Contact Information

Slack Team

This term we will be using Slack for class discussion. The system is highly catered to getting you help fast and efficiently from classmates and myself. Rather than emailing questions, I encourage you to post your questions on there. Find our class page at:

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Physics 472, Quantum Mechanics II, is the second semester of our two-semester sequence of junior-level quantum mechanics. For the spring 2021 offering, the course will be taught in a hybrid format online. The course activities that are planned reflect what makes an online course more engaging and more valuable to your learning. As always, we can discuss what is working for you and what isn’t openly.

Course Philosophy

For most of you, 472 is an elective course that you are taking to advance your knowledge of quantum mechanics. As such, this course is designed under several different principles than a standard course. Below, I provide those principles and their rationale.

  • 472 should help you learn the central tenets of Quantum Mechanics
    • This course provides the conclusion of the story started in 471. In 471, you learned about what separates quantum mechanics from classical mechanics through observations of Stern-Gerlach experiments; you learned some of the formalism of quantum mechanics through the concept of spin; and you begin to look at the time evolution of state vectors. In 472, we will build on that foundation to explore the position and momentum representation of quantum systems; we will investigate a larger theory of angular momentum for which spin plays a part; and we will investigate canonical examples of quantum systems like hydrogen atom and the quantum harmonic oscillator as well as what happens when we perturb them. This course should help you see how the basic formalism of quantum mechanics can be extended to more complex systems. Because quantum mechanics is such a broad topic, we will cover the canonical elements in class and you will research advanced topics and share them with your class mates.
  • 472 should be a celebration of your knowledge
    • For many of you, this course concludes your study of physics at MSU. What you have achieved in the last four years should be celebrated and enjoyed. This course will provide ample opportunities for you to share what things you know and what things you are learning with me and with each other.
  • 472 should give you opportunities to engage in professional practice
    • As you start towards your professional career, it’s important to learn what professional scientists do. You have probably already begun this work in advanced lab and research projects that you have worked on. We will continue developing your professional skills in this course through the use of final course projects in lieu of final exams.
  • 472 will illustrate that we can learn from each other
    • Even though I’ve been learning physics for almost 20 years, I don’t know everything. I am excited to learn from you and I hope that you are excited to learn from me and each other.

Required purchases:

Course Activities

Pre-class Preparation

As we are going to try to have an engaging online class experience, you will be asked to prepare weekly for class by reading sections from McIntyre, watching some short videos on the same topics, and replying to a pre-class survey about your understanding.

By doing this, you will have prepared yourself to discuss the concepts and the mathematics we are going to ues that week as well as reflect on what you know and what you are still needing to learn more about. In addition, you will be communicating that information to me, so that I can tailor activities for the week to address what you want more practice with and what you are still finding tough.

The calendar will be updated weekly with the readings, videos, and a reminder of the survey link. You will also be able to find links to the survey on D2L. To receive credit, you will need to post your response to the final question of the survey (what questions do you still have?) to the appropriate D2L assignment before 11:59pm on Sundays. These are graded for completion only. You may miss two without any grade penalty.

Class Meetings

We will meet three times weekly (MWF 12:40 PM - 1:30 PM Eastern Time) over Zoom. Attendance is not mandatory, but you are not likely to do well if you do not attend regularly. Experience has shown that students who attend and engage with class meetings tend to earn 3.5-4.0s in my upper-level class. I do want class meetings to be engaging and useful for you, too, so I will try to my best to make sure that is the case.

We will use a combination of large class meetings and breakout rooms. In large class meetings, I would appreciate if you were muted to cut down on background noise while others are speaking. You may use the chat, raise hand feature, or Slack as you see fit. Of course, you may also unmute yourself to ask a question or make a point. If you are comfortable with having your camera on during class, please do so. If not, please feel free to add an image of your liking (photo of yourself, illustration, etc.).

In class, we will typically start with a brief discussion of the pre-class survey and the questions that you posed. Any of you may engage in that discussion either by unmuting yourself or using the chat. We are then likely to spend some time in small groups working on an activity. These might be a conceptual problem, a calculation, part of a derivation, or something else related to the concept we are working on that day. I will prepare these as a handout that you can download during class. Afterwards, I will ask one group to present their work and ask any additional questions they have. For the last half of class, we will have an interactive lecture with some conceptual questions posed to you.

My aim for our class meetings is that you work with the mathematics and concepts that we are learning about and that you feel comfortable asking questions to further your own understanding.


There will be a homework due every Friday by 5pm. Late homework can’t be accepted once solutions are posted - but, your lowest score will be dropped. Homework is exceedingly important for developing an understanding of the course material, not to mention building skills in complex physical and mathematical problem solving. They will require considerable time and personal effort this term! Your lowest homework grade will be dropped.

There are two kinds of homework problems in this class:

Standard Homework Problems: These are regular back-of-the-book type homework problems that involve derivations, calculations, figures, and graphs. Although the problems that I tend to write ask for more explanation than book problems. If you took 481 or 482 with me, you have a sense of what they look like. Because there are so many students in this class, Each question will be coarsely graded for “completion”:

  • 10 pts. complete
  • 8 pts. right idea, but incomplete
  • 6 pts. fair amount of progress, but incomplete/incorrect
  • 4 pts. relatively incomplete/incorrect
  • 0 pts. not turned in

You will turn in homework sets using Gradescope. You can take photos of your homework or scan it. We would prefer that you start each homework problem (not part) on it’s own page or pages. That makes it easier for the grader to organize your problems.

Computational Homework Problems: There will be some use of computation in this course on homework problems. I will encourage and support the use of Python (through Jupyter notebooks). You do not need any computational experience for this course as you will learn some fundamentals early on and keep using them throughout the course. You are welcome to use any environment of your choosing (e.g., Octave/MATLAB, Mathematica, C++), but I will only provide support for Python. Python is in use across the sciences, but it is becoming much used in physics, so learning it will serve you well in your future work. I suggest downloading the Anaconda distribution of Python as it comes with all the packages you will need to get up and running with Jupyter notebooks. These will be graded on the same 10-8-6-4-0 scale as standard homework problems. Here are instructions for installing Jupyter Notebooks.

I strongly encourage collaboration, an essential skill in science and engineering (and highly valued by employers!) Social interactions are critical to scientists’ success – most good ideas grow out of discussions with colleagues, and essentially all physicists work as part of a group. Find partners and work on homework together. However, it is also important that you OWN the material. I strongly suggest you start homework by yourself (and that means really making an extended effort on every problem). Then work with a group, and finally, finish up on your own – write up your own work, in your own way. There will also be time for peer discussion during classes – as you work together, try to help your partners get over confusions, listen to them, ask each other questions, critique, teach each other. You will learn a lot this way! For all assignments, the work you turn in must in the end be your own: in your own words, reflecting your own understanding. (If, at any time, for any reason, you feel disadvantaged or isolated, contact me and I can discretely try to help arrange study groups.)

Help Session

Help sessions/office hours are to facilitate your learning. We encourage attendance - plan on working in small groups, our role will be as learning coaches. The sessions are homework-centric, but we will not be explicitly telling anyone how to do the homework (how would that help you learn?) I strongly encourage you to start all problems on your own. If you come to help sessions “cold”, the value of homework to you will be greatly reduced.

We will schedule these sessions after the first week of class.

Take-Home Quizzes

You will have take-home quizzes this semester that cover the material discussed in the previous few weeks. The quiz will take the form of a typical exam-style question – more straight-forward than your homework questions with not much substantive calculations. I will inform you of the type and topic of the in-class quiz on the a week prior to the quiz, so you will have a week to prepare should you want. Of course, the quiz is open note, open book, and open internet. You should not collaborate with other students on the quiz and any work you turn in, must be your own. You will have 24 hours to complete the quizzes. Quizzes will be turned in using Gradescope. There will five of these quizzes. Your lowest quiz grade will be dropped.

Quiz Re-writes

Once the quizzes are graded, if you would like to earn back 30% of the points that you lost. You may rework the quiz and explain what your thinking was at the time of the quiz and how it changed as a result of better understanding the topic. You may collaborate on quiz re-writes.

Final Project

In lieu of final exams, which are not at all representative of professional physics practice, you will produce a final project with a partner.

Pair Project

The final project is a team project that you will complete with a partner. It is meant to mimic the common practice of talk preparation and presentation. In a nutshell, you will conduct an original modeling project where you analytically and computationally model some quantum phenomenon of your choosing, prepare a talk on the project, and present it to your classmates and me using a recorded video. In working on this project, you will be trying to answer the following questions:

  • What is the area of quantum physics that you are doing research on?
  • What are the questions that you are trying to answer about this area?
  • What theoretical models can be used to answer those questions?
  • What analytical and computational work did you do to answer those questions?
  • What were the resulting predictions that your work produced?
  • What are the limitations of what you have done? What are some remaining open questions?
  • What did each member of your pair contribute?

Your video presentation is due the day of our final exam (we will not meet for the exam). You and your teammate will upload your talk for your classmates and myself. Your presentation will be graded by me. But, you will also be evaluated by your peers. Your participation in the evaluation of your classmates’ presentations counts towards your grade on your final. There will also be a self-reflection/evaluation component to this assignment that asks you: Who did what? What did you learn? What did you want to learn more about? What was straight-forward? What was more difficult? Completion of this self-reflection/evaluation will also count towards the overall grade on your final.

Grading the pair project

A rubric will be posted along with additional instructions soon.


Activity     Date     Percent of Grade
Weekly Pre-Class Preparation     Due Sunday night     10%
Homework (14 total; 1 dropped)     Due Fri by 5pm     40%
In-Class Quizzes (5 total; 1 dropped)     Roughly every 3 weeks     30%
Final Project     Mon Apr 26     20%

Comments on preparation:

Physics 472 covers material you might have seen before (Many of the topics stem from PHY 215 material) but at a higher level of conceptual and mathematical sophistication.

Therefore you should expect:

  • a large amount of material covered quickly.
  • no recitations, and few examples covered in lecture. Most homework problems are not similar to examples from class.
  • long, hard homework problems that usually cannot be completed by one individual alone.
  • challenging projects.

Physics 472 covers some of the most important physics and mathematical methods in the field. Your reward for the hard work and effort will be learning important and elegant material that you will use over and over as a physics major. Here is what I have experienced, and heard from other faculty teaching upper division physics in the past:

  • most students reported spending a minimum of 10 hours per week on the homework (!!)
  • students who didn’t attend the homework help sessions often did poorly in the class.
  • students reported learning a tremendous amount in this class.

The course topics that we will cover in Physics 472 are among the greatest intellectual achievements of humans. Don’t be surprised if you have to think hard and work hard to master the material.

Commitment to an Inclusive Classroom

I am committed to creating an inclusive classroom - one where you and your classmates feel comfortable, intellectually challenged, and able to speak up about your ideas and experiences. This means that our classroom, our virtual environments, and our interactions need to be as inclusive as possible. Mutual respect, civility, and the ability to listen and observe others are central to creating a classroom that is inclusive. I will strive to do this and I ask that you do the same. If I can do anything to make the classroom a better learning environment for you, please let me know.

If you observe or experience behaviors that violate our commitment to inclusivity, please let me know as soon as possible.

If I violate this principle, please let me know or please tell the undergraduate department chair, Stuart Tessmer (, who I have informed to tell me about any such incidents without conveying student information to me.

Confidentiality and Mandatory Reporting

College students often experience issues that may interfere with academic success such as academic stress, sleep problems, juggling responsibiities, life events, relationship concerns, or feelings of anxiety, hopelessness, or depression. As your instructor, one of my responsibilities is to help create a safe learning environment and to support you through these situations and experiences. I also have a mandatory reporting responsibility related to my role as a University employee. It is my goal that you feel able to share information related to your life experiences in classroom discussions, in written work, and in one-on-one meetings. I will seek to keep information you share private to the greatest extent possible. However, under Title IX, I am required to share information regarding sexual misconduct, relationship violence, or information about criminal activity on MSU’s campus with the University including the Office of Institutional Equity (OIE).

Students may speak to someone confidentially by contacting MSU Counseling and Psychiatric Service (CAPS) (, 517-355-8270), MSU’s 24-hour Sexual Assault Crisis Line (, 517-372-6666), or Olin Health Center (, 517-884-6546).

Spartan Code of Honor Academic Pledge

As a Spartan, I will strive to uphold values of the highest ethical standard. I will practice honesty in my work, foster honesty in my peers, and take pride in knowing that honor is worth more than grades. I will carry these values beyond my time as a student at Michigan State University, continuing the endeavor to build personal integrity in all that I do.

Handling Emergency Situations

In the event of an emergency arising within the classroom, Prof. Caballero will notify you of what actions that may be required to ensure your safety. It is the responsibility of each student to understand the evacuation, “shelter-in-place,” and “secure-in-place” guidelines posted in each facility and to act in a safe manner. You are allowed to maintain cellular devices in a silent mode during this course, in order to receive emergency SMS text, phone or email messages distributed by the university. When anyone receives such a notification or observes an emergency situation, they should immediately bring it to the attention of Prof. Caballero in a way that causes the least disruption. If an evacuation is ordered, please ensure that you do it in a safe manner and facilitate those around you that may not otherwise be able to safely leave. When these orders are given, you do have the right as a member of this community to follow that order. Also, if a shelter-in-place or secure-in-place is ordered, please seek areas of refuge that are safe depending on the emergency encountered and provide assistance if it is advisable to do so.