Quantum Mechanics

An excellent introductory quantum mechanics course, exposing students to the fundamentals of modern quantum physics.

The lectures for the first few chapters are borrowed from the "Quantum Mechanics for Everyone" course, but the problem sets go beyond the intuitive notions, forcing the learner to develop a mathematical mindset for quantitatively answering such questions. The remaining chapters develop a sophisticated mathematical apparatus, based on operator theory and Lie algebra formulas, useful for solving the Schrödinger equation in various contexts.

The course does at great job at combining theoretical and mathematical results with the physical intuitions and experiments behind them. The course starts from "the quantum mystery" and builds up all the way to perturbation theory, presenting along the way some applications to modern scientific developments such as the MRI machine or LIGO.

The most comprehensive of any introductory course on quantum mechanics.

It naturally includes particle spin and spin operators, which I've not seen included in any other course I've done on Quantum Mechanics or Electricity and Magnetism.

The early part covers the material in Quantum Mechanics for Everyone, followed by the more mathematical treatment using mostly matrices and operators rather than calculus, which helps in visualizing the physical processes involved.

It doesn't waste time indulging in philosophical speculation, nor does it get bogged down in technical details tailored to semiconductor design.

Some topics do need patience for their relevance to be revealed in later modules - a difficulty encountered by any math-heavy topic, but mostly it is self-explanatory.

Later modules do need more time investment than the beginner-friendly introductory modules, so you shouldn't take the initial modules as a reference for the time-load involved.

I didn't do the prerequisite mathematical subject and that made it a bit more difficult, but the entire notes of that math subject are included as a reference.

Recommended for anyone generally confident in their mathematical ability and scientifically curious.

This course absolutely deserves 5 stars. It is extremely well-organized, and covers a broad range of material. The professor, rather than a junior staff member, responds personally and promptly to all student inquiries, and sticks with you until you get whatever it was you hadn't been understanding. There are lots of practice problems, and the problem sets give you immediate feedback if your answer is mistaken, allowing you several attempts to get it right. (The policy for exams is a bit different.) I am a prof in a non-STEM field, and I am in awe of how this course is put together.

However, there are several things you should consider if you are a prospective student, or even if you've firmly decided to take the course.

1. This is not mainly a course about the mysteries of the Universe, space, time etc. There is somewhat more of that in the first 4 weeks, which you can take at a more leisurely pace as QM for Everyone, from the same professor. In this one, eventually you'll have to contend with lessons like calculating spherical harmonics using operator methods only, or recursion relations for hyperfine lines of the hydrogen spectrum. In at least 2/3 of the course content, lectures are mainly about the derivation of various equations. The prof has boundless enthusiasm for these endeavors, and some of them have very interesting applications; but you may have moments of wondering what's it all for.

2. This is not QM without calculus. You absolutely need to know calculus, including 1st-order linear differential equations. You also need a lot of linear algebra, and to feel comfortable working with complex numbers; there is even a little bit of complex contour integration. It uses *less* calculus and differential equation (DE) material than the usual approach to QM, but the necessary math skills are at a 2nd-year university level at least -- plus a lot of good intuition.

3. This course takes an "algebraic" approach, but that term refers to algebra as taught in university math departments, not high school algebra. It also signifies the distinction from the traditional DE-based approach mentioned above. "Algebraic" is not a synonym for "easy." Not so long ago, much of the material was traditionally taught in grad school. There may be some high school students who can complete this course, but that's like saying there are 14-year-olds who can get into MIT. It is possible for some individuals, but not a general rule.

4. More specifically, the material is based on an operator-based approach begun by Erwin Schrödinger in the 1940s, then back-burnered, then revived by particle physicists in the 1980s, and then extended by the prof in this course and his collaborators (among other groups). There aren't any textbooks following the approach used in this course. So if you're confused and you don't get the prof's explanation, you have very limited resources, even online. Because most texts follow the DE approach (Schrödinger's famous method from the 1920s) they're not so useful as references -- this even includes textbooks that, like this course, begin with a discussion of Dirac notation and electron spin, rather than wave mechanics. Also, they don't cover so wide a range of topics as this course. So, save your money. Two possible exceptions are Griffiths 3d ed. and Mark Fox's Quantum Optics, each of which can give you a big picture view of what's going on with some classic topics.

5. From week 5, the problem sets get longer and more difficult. They go up a further notch in the last couple of weeks, too (though Module 6, in the middle of the term, was also a bear). The midterms are somewhat easier, but the final is more mixed, with some long examples of what the prof likes to call "French cooking": very detailed calculations that are easy to mess up. Some of the problem set problems take a couple of days to get right; others just a few hours; few take less than an hour. Note that with automated grading, your answer is right or wrong: it may have taken you 2 days to get a result, but if one minus sign or factor of ħ is absent or misplaced, you get zero points. Problem sets will tell you when you're wrong, but you have a limited number of tries. On exams, you can change your answer as much as you like, but you get no guidance before it's too late (exam is over).

6. I am an older student, who also has a job and a family. The last time I'd taken a physics course of any kind was 30 years ago, and the last time I'd come near a QM course was 50 years ago (and I dropped it!). I found that this course both moves very quickly and demands a substantial time commitment. I spent far more than the projected 8-12 hours/week -- more like 15-20, easily -- and I was worried about passing, all the way up to the final. Very ordinary events, such as family and friends visiting from out of town, or the end-of-semester rush of work in the courses I teach, really messed up my progress in the course. And there were very few nights during the course I got to bed before 03:00.

I had other motivations than curiosity to take this course, and no particular interest in QM at all when I enrolled. My feelings about the course while working on it cycled through annoyance, interest and frustration on about an hourly basis. In the final weeks, I would gaze in anticipation at various non-physics books in my library that I could finally read when this course was over -- my rate of recreational and work-related reading had fallen by about 90% while the course was ongoing. And yet once it ended, and I could re-shelve the stack of QM books I'd kept by my desk for about 4 months, I held back one or two to read during my university's intersession break. If this course could get even a hard case like me interested in the subject, I don't have any hesitation in recommending it to someone who's already interested, provided you have the necessary math background and a strong work ethic.

This is a wonderful course, taught be a wonderful professor. I found it very challenging. I tried to prepare by reviewing all the math I had mastered a long time ago, but had not used for at least forty years; this was not enough. I was mostly ready but too much of the math needed appeared to be developed solely to solve quantum mechanics problems. Professor Freedericks did a great job helping to fill the math gap. The course had great balance with lectures, homework, tests, historical perspective and practical motivation. I’m taking the course at my own pace, to learn some physics, not for credit, and hope enough material will be available to me as an archived course to make the expense worthwhile. So far I’ve sure gotten my money’s worth. Thank you very much professor Freedericks.

Last year I successfully completed Prof. Freericks' courses on Mathematical and Computational Methods and now also the one on Quantum Mechanics. Both courses are outstanding but also very challenging and definitely worth the effort. Prof. Freericks' chooses the operator-focused approach to quantum mechanics, which allows the difficult subject to be grasped more intuitively than by solving complicated differential equations. Everything is explained in detail and can be consolidated and deepened in problems. In the first part of the quantum mechanics course, the illustrated simulations allow even beginners to approach topics such as the double-slit experiment, the Stern-Gerlach experiment, or Bell's inequality in a playful way, but on a sound basis. The theory will be further deepened during the course, so that I have ended the course with the good feeling of having received a solid foundation for further study of quantum mechanics.

A bit underwhelming up to the first midterm, but boy did it deliver. Make no mistake this is as challenging a QM undergrad class as it gets. You know, in good way. You can't get better without stepping out of the comfort zone, and this is the right amount of challenging yet accessible.It also goes out of its way to clarify important topics that are likely to be overlooked in the top qm textbooks out there, and as a result many of us might harbor missconceptions about! (Fair warning ,this is not for the uninitiated or the weak of math) Moreover, Jim ( professor Freericks) is just the nicest person ever. He's constantly active on the discussion forums. You' ll surely get a response within hours. He's quick to share resources and willing to discuss theory (within reason). He's been expanding this very algebraic method qm is taught in his class for a while, he is really passionate about it and he has a proven track record of collaborating with past alumni. I've also taken his Maths class and do wish he'd have the time and energy to offer more great courses and democratise higher education further for us enthusiasts. But enough brown nosing for now! 5 stars from me

This course is great . It is very well designed and run. It is quite remarkable how well this course transfers the rigors of a traditionally delivered course in quantum mechanics into an online format.

The class starts off fairly moderately paced. The material is by no means simple, but there are a lot of guided simulations of experiments, and the classwork really does build an understanding effectively.

The pace shifts partway through the course, and deepens considerably, or at least that's how it struck me. More of the instruction was delivered through lectures, through there were still helpful 'classwork' components. It was not as traditional as most university QM courses in terms of the methods used to develop an understanding of QM, and of problem solving. But it was by no means easy or simple.

If you want to learn deeply about how the quantum world works, this class is for you. The necessary math prerequisites are addressed in a companion math methods course. I am ~ 15 years removed from the 'advanced' math I took in college , and these courses together were an effective refresher on the math and introduction to the quantum mechanics material.

One thing I really appreciated were the problems, including ungraded 'classwork', end of unit problem sets, and exams. If you do these problems you will be forced to really work with the ideas in many ways. It's easy to be fooled into thinking one understands something because they can follow a derivation or explanation. This course is effective at making sure one really learns the material, through a good selection of types and difficulties of problems. Overall taking this course has been a highlight of this last five months.

This course is a great Quantum Mechanics course with one of the best professors in this field. Professor Freericks prepared a lot of materials and covered major aspects of QM. He also introduced new mathematical techniques and tricks to solve the problems in this pretty long and extensive course.
While it is extremely difficult for any instructor to summarize the most important aspects of Quantum Mechanics in one semester, the instructor did a wonderful job to encourage students to engage their mind by carefully crafting the ungraded and graded problem sets in each section of the course.
What I really appreciate of this course is, students are not only getting exposed to the complex concepts which can be forgotten easily but getting their hands dirty with the problems and thoroughly thinking, calculating, and solving them. The problem sets are accurately designed as the crucial part of the learning process as well as the lectures and visual materials. All of them help to understand the concepts deeply.
As a result, the course is built with all the modules together and connected in a way to reduce redundancies, hence, students can feel the course as a unified course.
The course has different prerequisites, specially for students who are from a different field of study. For example, I come from engineering background, it took me extra time to refresh, and study required math and tools. Therefore, this course required me a great commitment and dedication to finish. I certainly recommend this course to anyone who is looking to study Quantum Mechanics in deep.

This is an outstanding course taught by an outstanding instructor. Prof. Freericks teaching style is very inspirational and his enthusiasm for the subject is contagious. You will be well supported by the Professor if you take the trouble to express your doubts using the discussion forum. I have received replies to my questions and comments within an hour or two of posting - even during nights and weekends! If you are lucky, like I was, you may have some experienced physicists taking the course with you and supporting you through the discussion forum

Although rewarding, this is a difficult course. I would advise allocating 15-20 hours per week towards the course if you have no prior background in the subject. I have a Ph.D in chemical engineering with just the basic physics undergrad classes. For me, most of the learning happened when I solved the problem sets and the exams. I often had to go through the lectures very carefully and understand them to answer the questions.

Prof. Freericks teaches Quantum mechanics using Dirac notation and operators. Even though this limits the math, the notation itself takes time to understand and get used to. Nevertheless it was quite thrilling to learn this new "language". I definitely believe this course has laid a solid foundation for me to delve deeper into the subject.