Advanced Quantum Mechanics
Advanced Quantum Mechanics (Fall 2013, Standard Univ.). Taught by Professor Leonard Susskind, this course will explore the various types of quantum systems that occur in nature, from harmonic oscillators to atoms and molecules, photons, and quantum fields. Students will learn what it means for an electron to be a fermion and how that leads to the Pauli exclusion principle. They will also learn what it means for a photon to be a boson and how that allows us to build radios and lasers. The strange phenomenon of quantum tunneling will lead to an understanding of how nuclei emit alpha particles and how the same effect predicts that cosmological space can "boil." Finally, the course will delve into the world of quantum field theory and the relation between waves and particles. (from theoreticalminimum.com)
| Lecture 01 - Review of Quantum Mechanics and Introduction to Symmetry 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. |
| Lecture 02 - Symmetry Groups and Degeneracy Leonard Susskind presents an example of rotational symmetry and derives the angular momentum operator as the generator of this symmetry. He then presents the concept of degenerate states, and shows that any two symmetries that do not commute imply degeneracy. |
| Lecture 03 - Atomic Orbits and Harmonic Oscillators 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. |
| Lecture 04 - Spin Building on the previous discussion of atomic energy levels, Leonard Susskind demonstrates the origin of the concept of electron spin and the exclusion principle. |
| Lecture 05 - Fermions: A Tale of Two Minus Signs 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. |
| Lecture 06 - Quantum Field Theory Leonard Susskind introduces quantum field theory and its connection to quantum harmonic oscillators. Gravity aside, quantum field theory offers the most complete theoretical description of our universe. |
| Lecture 07 - Quantum Field Theory 2 Leonard Susskind extends the presentation of quantum field theory to multi-particle systems, and derives the particle creation and annihilation operators. |
| References |
| Advanced Quantum Mechanics (Fall, 2013) | The Theoretical Minimum This course will explore the various types of quantum systems that occur in nature, from harmonic oscillators to atoms and molecules, photons, and quantum fields. |