# PHYS2581 Foundations of Physics 2A (2018/19)

Details of the module's prerequisites, learning outcomes, assessment and contact hours are given in the official module description in the Faculty Handbook - follow the link above. A detailed description of the module's content is given below, together with book lists and a link to the current library catalogue entries. For an explanation of the library's categorisation system see https://www.dur.ac.uk/physics/students/library/

## Content

### Quantum Mechanics

21 lectures + 9 workshops in Michaelmas Term

*Textbooks:*

Required: Introduction to Quantum Mechanics, David J Griffiths, (Pearson/Prentice Hall, 2005, 2nd Edition).

The course is generally taught from material in this book, and chapter 6 (pertubation theory) is placed on DUO.

Additional: Quantum Mechanics, B.H. Bransden and C.J. Joachain (Prentice Hall, 2nd Edition)

The course is defined by material in this book and in particular the material defined in the syllabus below where the numbers refer to the sections in the book.

*Syllabus:*

- Summary of Level 1 Quantum Mechanics (the Schrödinger equation, the interpretation of the wave function, energy levels, plane waves)
- Wave packets and wave packet spreading [2.4]
- The momentum operator [2.3]
- Wave functions in momentum space; the delta function [2.4]
- The time-dependent Schrödinger equation [3.1]
- Conservation of probability [3.2]
- The Ehrenfest theorem [3.4] and the virial theorem [5.7]
- Stationary states [3.5]
- Example: the linear harmonic potential (energy levels and wave functions in terms of Hermite polynomials) [4.7]
- General solution of the time-dependent Schrödinger equation for a time-independent potential [3.8]
- Properties of the eigenfunctions of the Hamiltonian [3.7]
- Introduction to the formalism of quantum mechanics (quantum states, Dirac notation, dynamical variables and operators, eigenvalues and eigenvectors, expansion in eigenfunctions, expectation values) [3.3 and summary of Ch. 5]
- The Schrödinger equation in 3D Cartesian coordinates [7.1]
- The Schrödinger equation in spherical polar coordinates [7.2]
- Orbital angular momentum (differential operator) [6.1]
- Eigenfunctions and eigenvalues of
*L*and^{2}*L*; spherical harmonics and their properties [6.3]_{z} - The hydrogen atom (calculation of the energy levels and of the bound state wave functions, radial and angular distribution functions, reduced mass) [7.5]
- An introduction to spin, to 2-component spinors and to the addition of angular momenta [summary of 6.5, 6.8 and 6.10]
- The total angular momentum
**J**and the eigenvalues of*J*and^{2}*J*[6.9]_{z} - Time independent non-degenerate perturbation theory [8.1]
- Time independent degenerate perturbation theory [8.2 and Griffiths Ch. 6]
- Example: the Stark effect in the ground state and in the
*n = 2*states of atomic hydrogen [12.1] - Quasi-degenerate states [8.2]
- Spin-orbit coupling and the fine structure of hydrogen [8.3 and Griffiths 6.3]
- Hyperfine splitting [Griffiths 6.5]

### Electromagnetism

21 lectures + 9 workshops in Epiphany Term

*Textbooks:*

Required: Introduction to Electrodynamics, D.J. Griffiths (Pearson, 3rd Edition)

The course is defined by material contained in this book, in particular Chapters 2-9.

*Syllabus:* Electrostatics: The Electrostatic Field, Divergence and Curl of Electrostatic Fields, Electric Potential, Work and Energy in Electrostatics, Conductors. Special Techniques: Laplace's Equation and Uniqueness Theorems, The Method of Images, Separation of Variables, Multipole Expansion. Electrostatic Fields in Matter: Polarization, The Field of a Polarized Object, The Electric Displacement, Linear Dielectrics. Magnetostatics: The Lorentz Force Law, The Biot-Savart Law, The Divergence and Curl of B, Magnetic Vector Potential. Magnetic Fields in Matter: Magnetization, The Field of a Magnetized Object, The Auxiliary Field H, Linear and Nonlinear Media. Electrodynamics: Electromotive Force, Electromagnetic Induction, Maxwell's Equations. Conservation Laws: Charge and Energy, Momentum. Electromagnetic Waves: Waves in One Dimension, Electromagnetic Waves in Vacuum, Electromagnetic Waves in Matter, Absorption and Dispersion, Guided Waves.

### Revision

2 lectures in Easter Term, one by each lecturer

## Teaching methods

*Lectures:* 2 or 3 one-hour lectures per week.

*Workshops:* These provide an opportunity to work through and digest the course material by attempting exercises assisted by direct interaction with the workshop leaders. They also provide opportunity for you to obtain further feedback on the self-assessed formative weekly problems. Students will be divided into four groups, each of which will attend one one-hour class every week. The workshops for this module are compulsory.

*Mid-term progress tests: *Two 40-minute compulsory formative progress tests (weeks 6 and 16).

*Problem exercises:* See https://www.dur.ac.uk/physics/students/problems/