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Massachusetts Institute of Technology

Mastering Quantum Mechanics

Massachusetts Institute of Technology via edX


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

The first part reviews the basics of wave mechanics and introduces the variational principle. It then moves on to develop the technology of spin one-half states and spin operators. The last part of the module gives an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. The module concludes by developing the bra-ket notation of Dirac.

The second part covers Heisenberg’s uncertainty principle and the concept of compatible operators. It continues to develop the Heisenberg and the Schrödinger pictures of quantum mechanics. The module also covers the coherent and squeezed states of the harmonic oscillator. It concludes with two state systems and their applications to NMR and masers.

The third part introduces the concept of tensor product states to discuss entanglement and Bell inequalities. The module also covers angular momentum and the representations of angular momentum. This is used to understand the spectrum of central potentials and to introduce hidden symmetries. It concludes with the subject of addition of angular momentum and an algebraic approach to the hydrogen atom spectrum.

This course follows MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors.

Before starting, 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.

Completing the course provides the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics.

To master this course you will likely need a time investment of at least 12 hours a week.

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...
  • Nivvedan
    A lot of the material may seem like a repetition of the material covered in 8.04, but the level of rigor is much higher - you're truly introduced to the nature of the vector space that the quantum states live in and the operators that act on them, that were a little more hand wavy in 8.04. The treatment of Angular Momentum was extremely satisfying as a learning experience
  • 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.
  • 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.
  • 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.
  • 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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