Undergraduate

Quantum Mechanics I

A few words about the course

In this course, we will cover the basics of Quantum Mechanics. This is one of the modern theories in Physics that has been successfully explaining a broad range of phenomena for more than 100 years. It is difficult (arguably impossible) to understand Quantum mechanics in its fullest depth, so we do not plan to chase this dream here. Instead, we will try to learn the language of Quantum Mechanics and learn how to use this language to understand and explain quantum systems and quantum effects.

Resources

Here's a list of books and materials that could be helpful for this course. We may add more material as we proceed.

Quantum Mechanics, Concepts and Applications

by Nouredine Zettili

This will the main source of our course.

Principles of Quantum Mechanic

By Ramamurti Shankar

Quantum Mechanics Lecture notes

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.

Quantum Mechanics

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.

Lecture Notes

Lecture 1

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





Lecture 2

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.





Lecture 3

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





Lecture 4

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.





Lecture 5

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.






Assignment Set 2




Lecture 6

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.






Assignment Set 3




Lecture 7

In this note, we will cover some final details about the structure and postulates of QM.





Lecture 8

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.





Lecture 9

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.





Lecture 10

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.





Lecture 11

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.





Lecture 12

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.





Lecture 13

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.





Quantum Mechanics II

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.



QMII_Lecture 1

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.





QMII_Chapter 8: Identical Particles

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





QMII_Chapter 9: Time independent Perturbation Theory

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


QMII_Chapter 10: Time dependent Perturbation Theory

Now we get to the time-dependent perturbation theory.

Introduction and Interaction picture
Light Light-Matter Interaction


The course TAs

Roger Garfield

Pouyan Minaei

PhD student

    • Roger Garfield

    Moein Naseri

    MSc student