Unit information: Electromagnetism, Waves and Quantum Mechanics II in 2020/21

Unit name	Electromagnetism, Waves and Quantum Mechanics II
Unit code	PHYS20029
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Flaecher
Open unit status	Not open
Pre-requisites	PHYS10005, PHYS10006, or equivalent.
Co-requisites	None.
School/department	School of Physics
Faculty	Faculty of Science

Description including Unit Aims

Classical Physics comprises much of the core of physics, built on the foundations developed in the 17th to 19th centuries and underpinning all of ‘modern’ physics. This unit builds on the foundations from level C/4 in the areas of electromagnetic fields and waves. Maxwell's equations in vacuo and in simple solids form the basis of a discussion of fields, forces and energy for general charge and current configurations. Wave solutions of Maxwell’s equations are studied, relating the electromagnetic and optical properties of materials. General wave phenomena including interference and diffraction are investigated, along with practical applications of these effects.

This unit is the second formal introduction to quantum physics. Building upon the previous unit, it introduces for the first time the formal structure of quantum mechanics, including its principles and postulates. It covers the most famous of all quantum mechanical systems, the Hydrogen atom, and introduces the quantum mechanics of multiple particles.

Aims:

• to introduce students to a core of classical physics including electromagnetic fields and waves, wave interference and diffraction
• to introduce the formal mathematical structure of quantum mechanics. This will be applied to consider more advanced situations, including angular momentum, the hydrogen atom, and more than one particle

Intended Learning Outcomes

Students will:

• gain an appreciation of the broad thrust of classical physics and its wide applicability
• know Maxwell's equations. Be able to deduce from them the equations relevant to simple electrostatic cases and be able to solve problems in these cases
• be able to calculate the magnetic field from currents flowing in simple geometries
• understand the macroscopic descriptions of fields in conductors, dielectric materials and magnetic materials
• understand the description and properties of plane electromagnetic waves, in vacuum and in materials
• understand reflection and transmission of waves at interfaces
• explain features of the behaviour of fields in materials in terms of semi-classical microscopic models
• be familiar with the phenomena of interference and diffraction, and the principles of operation and practical uses of common types of interferometer
• Understand the notions of unit norm functions, normalisable functions, the superposition principle, and how normalisable functions form a vector space.
• Be able to define the scalar product between functions, some of its properties, and the definition of a Hilbert space.
• Be able to decompose a function into a basis of orthogonal functions and to change basis.
• Know what operators are, including linear, Hermitian and Unitary operators and Projection operators.
• Know what the adjoint of an operator is and be able to calculate matrix elements of operators.
• Be able to find the eigenvalues and eigenfunctions of operators and to understand the difference between degenerate and non-degenerate eigenvalues.
• Understand the time evolution of quantum states, and be able to write down the time evolution operator.
• Be able to state the postulates of quantum mechanics
• Be able to write down the angular momentum operators, calculate their commutation relations and find their eigenvalues and eigenstates.
• Be able to write down the Schrödinger equation in three dimensions with a central potential and understand what it means for angular momentum to be conserved in such situations
• Have an understanding of the energy eigenvalues and eigenstates of Hydrogen atom.
• Have a qualitative understanding of the quantum mechanics of other atoms and ions.
• Be able to write down and solve the Schrödinger equation for two non-identical particles in one or three dimensions.
• Be able to calculate joint probabilities, marginal probabilities, and to identify entanglement

Teaching Information

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises
• guided, structured reading

Assessment Information

Written timed, open-note examination (80%). Coursework (20%).

Reading and References

Essential:

• Griffiths - Introduction to Electrodynamics, Fourth edition 2014 (Pearson) - Electromagnetism
• Hecht – Optics

Further reading:

• Duffin - Electricity and Magnetism - copies in the university library
• Grant and Phillips - Electromagnetism
• A Rae – Quantum Mechanics
• DJ Griffiths – Quantum Mechanics