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Online Course

Mastering Quantum Mechanics

Massachusetts Institute of Technology via edX


The course offers a sophisticated view of quantum mechanics and its proper mathematical foundation. It will give you the tools needed to do research in quantum mechanics and to understand many current developments.

8.05 is the second semester of the three-course sequence on undergraduate quantum mechanics at MIT. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors. The online course 8.05x will follow the on-campus version and will be equally rigorous.

To master this material and to follow the course, you will likely need a time investment of ten to twelve hours a week. There will be weekly homework, one mid-term test, and a final exam.

Topics covered

Review of wave mechanics. Variational principle. Spin operators and general spin one-half states. Elements of linear algebra: complex vector spaces and linear operators. Hermitian operators and unitary operators. Dirac bra-ket notation. The uncertainty principle and compatible operators.

Schrodinger equation as unitary time evolution. The Heisenberg picture of quantum mechanics. Coherent and squeezed states of the harmonic oscillator. Two-state systems. Nuclear magnetic resonance and the ammonia maser.

Multiparticle states and tensor products. Entanglement and quantum teleportation. The Einstein, Podolsky, Rosen paradox and Bell inequalities. Identical particles: bosons and fermions.

Angular momentum and central potentials. Representations of angular momentum. Hidden symmetries and degeneracies. Addition of angular momentum. Algebraic solution of the hydrogen atom.

More on Prerequisites

To follow this course you will need some basic familiarity with quantum mechanics. You must have seen the Schrodinger equation and studied its solutions for the square well potential, the harmonic oscillator, and the hydrogen atom. You may have learned this by self-study or by taking an introductory one-quarter or one-semester course on the subject. You must be proficient in calculus and have some knowledge of linear algebra.


  • Who can register for this course?
    • Unfortunately, learners from Iran, Sudan and the Crimea region of Ukraine will not be able to register for this course at the present time.
    • While edX has received a license from the U.S. Office of Foreign Assets Control (OFAC) to offer courses to learners from Iran and Sudan our license does not cover this course.
    • Separately, EdX has applied for a license to offer courses to learners in the Crimea region of Ukraine, but we are awaiting a determination from OFAC on that application.
    • We are deeply sorry the U.S. government has determined that we have to block these learners, and we are working diligently to rectify this situation as soon as possible.

Taught by

Saif Rayyan and Barton Zwiebach


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4.9 rating, based on 8 reviews

Start your review of Mastering Quantum Mechanics

  • Anonymous

    Anonymous completed this course and found the course difficulty to be hard.

    This course really does what its title implies. If you strive to do a course in which you not only get a glimpse into the mathematics and the philosophy of QM, but you are serious to work hard to actually MASTER the stuff, this course is for you. But...
  • Anonymous

    Anonymous is taking this course right now.

    Difficulty level is Hard but very satisfying course especially after solving very insightful problems.The title of the course really means what it means especially the "mastering" part ,so it assumes fair amount of technical background as mentioned in course description .After completing this you will gain confidence to study other topics in QM on your own. Also gives QM background so that one can start reading research papers on their own in the interdisciplinary fields like Quantum information,computing,control and filtering if you have already have background EECS.I have taken this course because I wanted to specialize in Quantum control and filtering theory as I have a background in EE.
  • James Bullen is taking this course right now.

    Although I could not complete the course, I found it to be the most challenging and best course I have taken. I quickly realized that my knowledge base was not sufficient so I had to go back and take other excellent MIT OCW calculus, differential equation, linear algebra courses. I thought I had saved a copy of the problem set solutions to help me when I got back to studying the archived course.
    My flash got corrupted -- does anybody out there have a copy of the solutions?
    I am looking forward to the 8.04 course starting in September.
  • Anonymous

    Anonymous completed this course.

    Exiting and challenging. This course gave me an actual clue of what quantum mechanics means. Highly recommended. It supposed to be the minimum a graduated in physics should now.
  • Mauro Lacy completed this course, spending 18 hours a week on it and found the course difficulty to be hard.

    This is one of the best series, if not the best series of MOOC courses I've ever taken. Highly recommended.
  • Stojan Karlusic

    Stojan Karlusic completed this course.

  • Profile image for Radosław Kotkiewicz
    Radosław Kotkiewicz

    Radosław Kotkiewicz completed this course, spending 12 hours a week on it and found the course difficulty to be hard.

  • Nishant Gaikwad is taking this course right now.

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