# Unit information: Electromagnetism, Waves and Quantum Mechanics II in 2022/23

Unit name Electromagnetism, Waves and Quantum Mechanics II PHYS20029 20 I/5 Teaching Block 2 (weeks 13 - 24) Dr. Barnes Not open PHYS10005, PHYS10006, or equivalent. None. PHYS20020 Classical Physics II: Electromagnetism and Waves. School of Physics Faculty of Science

## Unit Information

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

## Your learning on this unit

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.
• Be able to write down the Schrödinger equation in three dimensions in Cartesian and in spherical polar coordinates.
• Be able to separate variables to obtain the radial and angular equations, and to appreciate the role of spherical harmonics as solutions to the latter when there is spherical symmetry.
• Be able to solve the Schrödinger equation for the three-dimension infinite box and to understand what it means to have degenerate energy eigenstates.

## How you will learn

The unit will be taught through a combination of

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

## How you will be assessed

Examination (80%). Coursework (20%).

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHYS20029).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.