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.

Professor Susskind uses the quantum mechanics of angular momentum derived in the last lecture to develop the Hamiltonian for the central force coulomb potential which describes an atom. The solution of the Schrödinger equation for this system leads to the energy levels for atomic orbits. He then derives the equations for a quantum harmonic oscillator, and demonstrates that the ground state of a harmonic oscillator cannot be at zero energy due to the Heisenberg uncertainty principle.

Recorded on October 7, 2013.

- Angular momentum multiplets
- Coulomb potential
- Central force problem
- Atomic orbit
- Harmonic oscillator
- Heisenberg uncertainty principle

1. Review of quantum mechanics and introduction to symmetry
2. Symmetry groups and degeneracy
3. Atomic orbits and harmonic oscillators
4. Spin, Pauli Matrices, and Pauli Exclusion Principle
5. Fermions: a tale of two minus signs
6. Quantum Field Theory: Particle Creation and Annihilation Operators
7. Quantum Field Theory: Fermions and Bosons
8. Second Quantization
9. Quantum Field Hamiltonian
10. Fermions and the Dirac equation

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.