by Nouredine Zettili

This will the main source of our course.

By Ramamurti Shankar

by Vahid Karimpour

These lecture notes are extremely well-written and cover the materials of this course in great details. You can also find the video lectures thought by Prof. Karimpour on-line. Both are extremely recommended.

by Claude Cohen-Tannoudji, et al.

This is also a great resource if you have the time. It covers a lot of details that we cannot get to in the class.

This lecture covers some introductory remarks, including a brief history of QM and then sets the stage for our discussion of wave-particle duality.

We investigate the behavior of light in the double-slit experiment as well as the Mach-Zehnder's interferometer and face the strange behviour of the quanta of light, a.k.a photon.

This lecture will cover the Stern-Gerlach Experiment and its significance in Quantum Mechanics.

In this lecture, we will find a mathematical description that can explain the Stern-Gerlach Experiment. This sets the foundations for Quantum Mechanics and will ease our way to stating the postulates of Quantum Mechanic.

In this lecture, we will use the mathematical description that was established for the Stern-Gerlach Experiment to make some postulates for Quantum Mechanic. We will also cover the Bra and Ket (Dirac) notation as well as some mathematical tools that we will be using throughout this course.

One of the key representations that we work with in QM, are based on the eigenvectors of the position and momentum spaces. In this lecture, we will learn more about continuous Hilbert spaces and start to work with the state in position and momentum space. Eventually we use these materials to get to the Schrodinger's equation.

Now we start applying QM to some simple 1-D potentials. These include the free particle, potential barrier and well and eventually we will get to the Harmonic Oscillator.

Next, we will get to the Harmonic Oscillator which is one of the most important models that we deal with this course and has practical applications in different branches of physics.

Our next lecture is on angular momentum. As we know from classical mechanics, angular momentum generates rotation. So beside its natural significance, we need to study rotational symmetry. This will help us investigate more complicated models in 3D that due to full rotational symmetry are still effectively one dimensional.

Now we get to 3D potentials. We will revisit some of the problems that we studied in lectures 8 and 9 but in 3 dimensions.

For the final section of this course, we get to the 3D potentials in spherical coordinates. We will derive the radial Schrodinger's equation
and revisit some of the examples the we solved in the Cartesian coordinates.

The final problem that we study is the Hydrogen atom which is on the border of what can be exactly solved in QM.
We will come back to this problem in QM II and investigate it in more details, but for now, we only include the
Coulomb potential and solve the radial Schrodinger's equation.

The videos of some of the lectures are posted here.

Please note that these videos are not prepared professionally and may contain typos, mistakes or have some other issues. If you come across any problem, please send me an email.

Please note that these videos are not prepared professionally and may contain typos, mistakes or have some other issues. If you come across any problem, please send me an email.

Next, we get to addition of angular momentum. In this lecture, we'll cover some of the basics of the representation theory and
learn about a new basis that instead of the quantum numbers of the individual subsystems of a composite system, is expressed in terms of the global propertis of the full composite system, namely the total angular momentum and total angular momentum in the z direction.

In this chapter, we will study identical particles in QM and see that, in contrast to classical physics, they can be fundamentally indistinguishable.

Our next stop is perturbation theory. This is one of the main approaches we take to solving/approximating models and systems that are too complex or challenging to be solved exactly.

Non-degenerate Perturbation Theory |

Degenerate Perturbation Theory |

Validity of the Perturbation Theory |

Revisiting the Hydrogen Atom |

Variational Methods |

WKB Approximation |

Now we get to the time-dependent perturbation theory.

Introduction and Interaction picture |

Light Light-Matter Interaction |