Unit information: Quantum Physics 301 in 2015/16

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Unit name Quantum Physics 301 PHYS32011 10 H/6 Teaching Block 1 (weeks 1 - 12) Dr. Furqaan Yusaf Not open 120 credit points at Level 5/I in Physics, Physics with Astrophysics, joint honours in Mathematics and Physics or Physics and Philosophy, or Chemical Physics programmes. None School of Physics Faculty of Science

Description

In the first half this course, we will give a more formal basis for the subject of Quantum Mechanics. This starts with a discussion of Dirac Notation, which is a particularly efficient way of working with the formalism of quantum mechanics. Using Dirac notation, we will formulate the principles and rules of quantum mechanics, and see how they apply to real physical situations.

Some of the elementary systems that you already know from your second year quantum mechanics course will then be covered again, in much more detail. These include spin-1/2, the harmonic oscillator and the angular momentum states of, for example, the hydrogen atom.

In the second half of the course, we will use the newly learned formalism to study real-life applications of quantum mechanics. We will find that the description of many systems is too complicated to be solved exactly. We will introduce several powerful approximation techniques to deal with these situations.

We will conclude by considering the role of time evolution in quantum mechanics, and its connection to symmetries, conservation laws, and approximation schemes for dynamical systems.

At the end of the course, you will have a good understanding of what all these topics entail, and you will be able to perform calculations in all of these subjects by yourself.

Intended learning outcomes

Students will be able to:

• phrase and analyse any problem in quantum mechanics within the formalism of Dirac notation.
• use the mathematical structures used by Dirac notation to do practical calculations.
• explain why approximation techniques are required to solve generic quantum mechanical problems and indicate when and how these techniques must be applied.
• formulate problems and perform calculations within the variational principle, perturbation theory, degenerate perturbation theory and time-dependent perturbation theory.
• analyse the time-dependence of quantum mechanical systems, in any one of its three pictures
• explain the relation between perturbation theory and the roles of time evolution and symmetry transformations in quantum mechanics.

Teaching details

Lectures, problems classes

Assessment Details

Written examination comprising 1 2-hour paper

There are many text books on Quantum Mechanics, but none of them follow precisely the structure of this lecture course. The first point of reference should therefore always be the (extensive) set of lecture notes for this course, which will be made available online.

In addition to the lecture notes, you should be able to find a discussion of any topic we cover during the lectures in one of the standard text books on quantum mechanics. The book that has most overlap with the course is:

• Modern Quantum Mechanics, by JJ Sakurai. A clear and thorough text that uses Dirac notation from the start.

Other recommended books include:

• Introduction to Quantum Mechanics, by DJ Griffiths for a fairly elementary, but often very clear and accessible discussion
• The principles of Quantum Mechanics, by PAM Dirac for a historic perspective by one of the founding fathers of the subject. This book was written in 1930, but it is still remarkably readable, and current
• Quantum Mechanics, by A Messiah (2 volumes) as a reference book. This is a very thorough and detailed discussion of all of quantum mechanics. It is not so useful as a text book to learn from, but a very good source of information if you want to look up more details on any of the subjects we will cover.
• Quantum Mechanics by AIM Rae, or Quantum Mechanics by F Mandl, or Introduction to Quantum Mechanics by AC Phillips, for basic texts that cover various parts of the material that we will discuss
• Quantum Physics by S Gasiorowicz, or Quantum Mechanics: Concepts and Applications by N Zettili, for slightly more advanced discussions.