Advanced Quantum Mechanics

Leonard Susskind concludes the course by generalizing the presentation of the quantum field theory for spin-1/2 fermions to three dimensions, and demonstrating that the mass of fermions originates from the cross term between the two chiralities in the Dirac equation.

Leonard Susskind develops the quantum field Hamiltonian, and then derives the Dirac equation for fermions. Dirac's theory of fermions was the first to incorporate special relativity into the development of quantum mechanics.

Leonard Susskind completes the discussion of quantum field theory and the second quantization procedure for bosons.

Leonard Susskind extends the presentation of quantum field theory to multi-particle systems, and derives the particle creation and annihilation operators.

Leonard Susskind introduces quantum field theory and it's connection to quantum harmonic oscillators. Gravity aside, quantum field theory offers the most complete theoretical description of our universe.

Leonard Susskind derives the energy levels of electrons in an atom using the quantum mechanics of angular momentum, and then moves on to describe the quantum mechanics of the harmonic oscillator.

Building on the previous discussion of atomic energy levels, Leonard Susskind demonstrates the origin of the concept of electron spin and the exclusion principle.

Leonard Susskind introduces the spin statistics of Fermions and Bosons, and shows that a single complete rotation of a Fermion is not an identity operation, but rather induces a phase change that is detectable.

Leonard Susskind presents an example of rotational symmetry and derives the angular momentum operator as the generator of this symmetry. He then discusses symmetry groups and Lie algebras, and shows how these concepts require that magnetic quantum numbers - i.e. spin - must have whole- or half-integer values.

After a brief review of the prior Quantum Mechanics course, Leonard Susskind introduces the concept of symmetry, and present a specific example of translational symmetry.