Welcome! Here you will find information and extra material for the course "Quantum theory in a Nutshell" given @AIMS Ghana 2021. Unfortunately, due to the global situation, the lectures will happen online.
Lecturer: Antonio D. Pereira
Contact: adpjunior@id.uff.br or A.Duarte@science.ru.nl
Feel free to write an e-mail to me with questions. I will try to collect questions and answer them during the lectures. If time does not permit that, I will reply to your e-mail privately.
There are several very good books on the topic and you can probably find one that you like most. I will use different books for the preparation of the lectures. Some texts that I like or I judge to be useful for you are
"Modern Quantum Mechanics" - J. J. Sakurai
"Introduction to Quantum Mechanics" - D. Griffiths
"Quantum Mechanics", Vol. 1 - C. Cohen-Tannoudji
"Quantum Physics of atoms, molecules, solids, nuclei, and particles" - R. Eisberg and R. Resnick
"Curso de Física Básica" - Volume 4 - H. Moysés Nussenzveig (unfortunately, this book does not have a translation to English)
I will also provide some notes and/or specific references for each different topic that we will cover.
Lecture 1: Introduction to the course; overview of "classical physics"; introduction to blackbody radiation. See virtual blackboard here.
Lecture 2: Blackbody radiation; Planck & quantization of energy; Planck's constant; Einstein & the photoelectric effect. See virtual blackboard here.
Lecture 3: Einstein & the photoelectric effect; Compton & the Compton shift. See virtual blackboard here.
Lecture 4: Rutherford & the Nucleus; Atomic spectra; Fraunhofer lines, absorption spectrum & emission spectrum; exercises. See virtual blackboard here.
Lecture 5: Bohr & the hydrogen atom; de Broglie & waves of matter. See virtual blackboard here.
Lecture 6: Recap of week 1, Particle-wave duality, double-slit experiment. See virtual blackboard here.
Lecture 7: Double-slit experiment with classical particles and electrons; Schrödinger wave function; Born's interpretation. See virtual blackboard here.
Lecture 8: Polarization of light; Photons and quantum states; Bra and Kets; Normalization condition. See virtual blackboard here.
Lecture 9: Different representations of the same state vector; recap of complex numbers; Starting with the postulates of quantum mechanics; measurements and probabilities. See virtual blackboard here.
Lecture 10: Quantum states associated with circular polarization; introduction to observables; expectation value. See virtual blackboard here.
Lecture 11: Expectation value of an operator; Outer product; Superposition; Resolution of the identity; Projectors. See virtual blackboard here.
Lecture 12: Q&A; Matrix representation of an operator; Hermitian conjugate of an operator. See virtual blackboard here.
Lecture 13: Hermitian matrices; Postulates for observables; Polarization as an observable; Introduction to uncertainty relations. See virtual blackboard here.
Lecture 14: Uncertainty relations; (In)compatible Observables; Position and momentum operators; canonical commutation relation See virtual blackboard here.
Lecture 15: Wave function; Position and momentum operators in position space representation; Schrödinger equation; Simple Harmonic Oscillator. See virtual blackboard here.
"Dr. Quantum" animation about the double-slit experiment can be found here. Don't take the explanations in the video too seriously but rather focus on the different outcomes of the double-slit experiment! ;)
Paper by W. Bragg with the very interesting quote: "There must be some fact of which we are entirely ignorant and whose discovery may revolutionize our views of the relations between waves and ether and matter. For the present we have to work on both theories. On Mondays, Wednesdays, and Fridays we use the wave theory; on Tuesdays, Thurs- days, and Saturdays we think in streams of flying energy quanta or corpuscles. That is after all a very proper attitude to take. We cannot state the whole truth since we have only partial statements, each covering a portion of the field. When we want to work in any one portion of the field or other, we must take out the right map. Some day we shall piece all the maps together ". See the full paper here.
I recommend reading Chapter 1 of Volume 3 of the famous "Feynman Lectures on Physics". It is available online here.