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Massachusetts Institute of Technology

Mastering Quantum Mechanics Part 3: Entanglement and Angular Momentum

Massachusetts Institute of Technology via edX

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This physics course introduces the concept of tensor product states to discuss entanglement and Bell inequalities. You will learn about angular momentum and its representations. This is used to understand the spectrum of central potentials and to introduce hidden symmetries. Lastly, you will learn about the addition of angular momentum and an algebraic approach to the hydrogen atom spectrum.

This is the last of three courses offering a sophisticated view of quantum mechanics and its proper mathematical foundation.

  • Part 1: Wave Mechanics
  • Part 2: Quantum Dynamics
  • Part 3: Entanglement and Angular Momentum

To follow this course you should have taken Part 1: Wave Mechanics, and Part 2: Quantum Dynamics.

Completing the 3-part Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics

The series will follow 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.


Week 1:

  • Multiparticle states and tensor products
  • Entanglement and quantum teleportation

Week 2:

  • The Einstein, Podolsky, Rosen paradox and Bell inequalities 
  • Representations of angular momentum

Week 3:

  • Angular momentum and central potentials

Week 4:

  • Hidden symmetries and degeneracies
  • Addition of angular momentum

Week 5:

  • Algebraic solution of the hydrogen atom

Final Assessment

Taught by

Barton Zwiebach and Saif Rayyan


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  • Third part of MITx 8.05x series of lectures on Quantum Mechanics, in which entanglement and angular momentum are thoroughly explained and exemplified. Multi-particle systems and tensor products, Bell's inequality, addition of angular momentum, spin-orbit coupling, the full spectrum of the Hydrogen atom, and much more.

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