Quantum Mechanics II – Summer 2018

PEU 348 Quantum Mechanics II – Summer 2018 

Prerequisite: PEU 323.

Schedule: 

Thursday  09:00 – 12:00;  Zewail City New Camp, Service Building, Room G006B
Wednesday  12:45 – 15:45;  Zewail City New Camp, Service Building, Room G006B

A very Informal introduction

The physical world exists, as far as we can tell, in three dimensions; so it is natural after having studied quantum mechanics in 1D to extend it to three dimensions, in order to apply it to atoms, molecules, solar cells, human cells, … you name it. The simplest atom to study is the Hydrogen atom. Since electrons have angular momentum (orbital and intrinsic), it turns out that it is crucial to have a quantum treatment of the angular momentum in order to understand how electrons behave. As if what you know about quantum mechanics so far is not weird enough, quantizing the angular momentum will introduce many new bizarre effects that we will try to touch in this course.
Afterwards, we shall learn that all quantum particles fall into one of two categories, fermions and bosons, each follows different kind of statistics (well, you may also have heard of anyons!). This statement has powerful consequences that extends from the photons that touch your eye all the way down to the smallest of the elementary particles discovered in the Large Hadron Collidor. We will study some of these consequences. A very important area where quantum mechanics is applied is solids. We will study basic models of solids such as free electron gas, Bloch band theory.
Finally, ‘enter: Time-Independent Perturbation Theory’; a very powerful method that most, if not all, quantum physicists have used once to solve real quantum problems. The basic idea is that many actual problems, with all the ‘dust and dirt’ implied by ‘actual’ can be treated as a neat system plus a small amount of perturbation. This fact will help us refine our understanding of the energy levels of the Hydrogen atom until we dig down to the ‘hyperfine’ splitting of its eigenstates.
I hope at the end of this course to have some time to talk about some foundational topic that is closer to current research.

Topics:
. Quantum Mechanics in 3D – The Hydrogen atom
. Angular Momentum and Spin
. Identical Particles and solids
. Time-Independent Perturbation Theory
. Additional topics

Detailed syllabus

Main textbook: David J. Griffiths, Introduction to Quantum Mechanics, 2nd Edition.
Other textbooks:
Modern Quantum Mechanics – J. J. Sakurai
Quantum Mechanics – Ballentine
Introductory Quantum Mechanics – Richard Liboff
Quantum Mechanics – Concepts and Applications. 2nd ed. Nouredine Zettili
Quantum Mechanics , 3rd ed. – Eugen Merzbacher
Quantum Mechanics 3rd ed. – Alastair I. M. Rae
Quantum Mechanics, by Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe
Applied Quantum Mechanics, 2nd edition, A. F. J. Levi
Quantum theory concepts and applications – Asher Peres

Useful online resources

1- MIT courseware
2- Physics StackExchange
3-Feynman lectures in physics
4-Math, Physics, and Engineering Applets

Videos

  1.  2p-1s transition
  2. Stern and Gerlach experiment

Useful lecture notes

  1.  Quantum mechanics in 3D
  2. Particle Spin and the Stern-Gerlach Experiment
  3. Time-Independent Degenerate Perturbation Theory
  4. Quantum Computing

Papers

  1. Planck’s Law and Light Quantum Hypothesis. N. S. Bose
  2. Bose’s letter to Einstein

 

 

Course Learning Objectives

1-Be able to generalise quantum problems in 1D to 3D
2- Choose the coordinate system suitable for the problem and make use of the symmetry to express the wave function in a simple form
3- Characterize the properties of a Hydroge Hydrogen atom in a certain eigenstate, given the quantum numbers of this state.
4- Express the angular momentum state of two or more particles in terms of the state of each one of them individually
5-Apply perturbation theory to solve various problems, such as a magnetic field interacting with Hydrogen atom
6- Understand the origin of the hyperfine structure
7- Apply the principles of quantum mechanics to solids
8- Differentiate between the two types of statistics for fermions and bosons and the macroscopic consequence of each

 

Homework policy:

Every week there will be a new assignment that should be handed in within the following week.
Assignments should be solved independently. Plagiarism will be heavily penalised. (No kidding here!)

Grading system

Assignments                 20%
Attendance and quizzes         5%
Midterm exams:           40%  Weighted Average of the two Midterms (60% of the best, 40% of the worst)
Final exam                 25%
Seminar 10%

No makeups for midterms.

Seminar topics

Bohmian mechanics
Quantum mechanics in phase space
Path integral formalism of quantum mechanics
Bell’s theorem
Bose-Einstein condensates
Cold atoms in optical lattices
Introduction to quantum computing
Weak measurement
Aharonov-Bohm effect
Time crystals
Quantum chaos
Two level systems (double well)
Adiabatic theorem
Realizations of Schrodinger’s cat states