PHY3055 Electromagnetism and Quantum Mechanics 2023-24
Dr E. Mariani

Delivery Weeks: T1:01-11
Level: 6 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 60 students (approx)

### Description

This module is taken by BSc students in stage 3. It develops students' knowledge of electromagnetism, quantum mechanics and illustrates the aspects in common and relationships between the two areas. It builds on the Stage 2 core modules PHY2021 (Electromagnetism I) and PHY2022 (Quantum Mechanics I). The starting point is the Maxwell equations introduced in PHY2021, which are manipulated to obtain the electromagnetic wave equation and the form of the solutions.

The dielectric and magnetic properties of atoms and materials are considered from both a classical and quantum perspective, with emphasis on the frequency dependence of their real and imaginary components, and the consequences for wave propagation. Wave propagation at interfaces between dissimilar materials is considered, leading to derivation of Fresnel reflection and transmission coefficients. Methods of guiding electromagnetic waves of different frequency by transmission lines, waveguides and optical fibers are discussed and this knowledge, along with the theory of quantum transitions is used to understand maser and laser operation.

This is a core module for BSc Physics programmes and is supported by BSc Stage 3 tutorials.

### Module Aims

The module aims to develop students' understanding of quantum mechanics and Maxwell's equations and their applications including some advanced topics, fomalism and applications to the point where they will be able to engage with contemporary research literature. Students will gain an in-depth understanding number of interesting physical phenomena that are important in a wide variety of areas and in many key technologies.

### Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
1. describe the fundamental aspects of electromagnetism;
2. explain and solve problems involving the magnetic and/or dielectric properties of materials;
3. explain some aspects of the interaction of electromagnetic radiation with matter;
4. calculate the effect of such interactions using appropriate vector mathematics;
5. solve problems requiring application of Maxwell's equations to a variety of situations as outlined in the syllabus below;
6. formulate, and evaluate, the solutions to a variety of perturbed and multi-electron quantum mechanical systems;
7. calculate energy shifts, transition probabilities (and rates) and cross-sections;
• Discipline Specific Skills and Knowledge:
1. use vector analysis to solve problems in science and engineering;
2. use matrix concepts to solve QM problems;
3. use mathematics to solve problems;
4. present and defend their solutions to problems to their tutorial group;
• Personal and Key Transferable / Employment Skills and Knowledge:
1. develop and present a coherent solution to a problem;
2. self-evaluate, check and correct solutions to problems;
3. undertake co-operative learning by discussing the contents of the module amongst themselves;
4. make informal presentations of technical material;
5. work independently in order to meet deadlines.

### Syllabus Plan

1. ELECTROMAGNETISM
1. Maxwell's Equations and Electromagnetic Waves
1. Maxwell's equations for the electromagnetic field and constitutive equations
2. The equation of continuity
3. Electromagnetic plane waves in an insulating isotropic medium
4. Polarization, momentum and energy, the Poynting vector
5. Scalar and vector potentials
6. Gauge invariance, the Coulomb and Lorentz gauges
2. Electromagnetic materials
1. Classical description of atomic polarisability, dispersion
2. Metals and the skin effect
3. Diamagnetism, paramagnetism and ferromagnetics: general concepts
4. Langevin (classical) theory of paramagnetism and electron paramagnetism
5. M–B loops
3. Electromagnetic waves at boundaries and guiding waves
1. Examples of metallic waveguides: cylindrical, rectangular
2. Coaxial cables and distributed impedance: the Telegrapher's equations
3. Fresnel's equations and their optical consequences
2. QUANTUM MECHANICS
1. Heisenberg's Approach to Quantum Mechanics
1. Matrix elements for a quantum harmonic oscillator
2. Electron spin and Pauli matrices
2. Few-Particle Systems
1. Bose and Fermi particles, the Pauli principle
2. Two-electron system: spin addition and exchange interaction
3. Structure of Many-Electron Atoms
1. Electron shells
2. Hund's rules,
3. The role of spin-orbit interaction
4. LS coupling scheme.
5. Zeeman effect in many-electron atoms
4. Quantum Transitions
1. Perturbation theory
2. Fermi's golden rule formula
3. Rate of spontaneous emission
4. The ruby laser

### Learning and Teaching

#### Learning Activities and Teaching Methods

Description Study time KIS type
20×1-hour lectures 20 hours SLT
2×1-hour problems/revision classes 2 hours SLT
3×1-hour tutorials 3 hours SLT
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 79 hours GIS

#### Assessment

Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-10 Discussion in tutorials
0% 4 × Problems sets 4 hours per set Fortnightly 1-10 Solutions discussed in problems classes.
100% Final Examination 2 hours 30 minutes January 1-10 Mark via MyExeter, collective feedback via ELE and solutions.

### Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

Supplementary texts:

ELE:

### Further Information

#### Prior Knowledge Requirements

Pre-requisite Modules Electromagnetism I (PHY2021) and Quantum Mechanics I (PHY2022) none

#### Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment Form of re-assessment ILOs re-assessed Time scale for re-assessment
Whole module Written examination (100%) 1-10 August/September assessment period

Notes: See Physics Assessment Conventions.

#### KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 25 hrs
GIS - guided independent study 125 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 0%
Written exams 100%
Practical exams 0%
Total 100%

#### Miscellaneous

 IoP Accreditation Checklist EM-04 Maxwell's equations and plane electromagnetic wave solution; Poynting vector EM-06 Polarisation of waves and behaviour at plane interfaces QM-05 Wave function and its interpretation QM-06 Standard solutions and quantum numbers to the level of the hydrogen atom QM-09 Quantum structure and spectra of simple atoms QM-12 Pauli exclusion principle, fermions and bosons and elementary particles SS-07 Magnetic properties of matter Availability BSc only Distance learning NO Keywords Physics; Maxwell's equations; Electromagnetic fields; Radiation; Properties of matter; Waves; Dirac notation; Energy; Eigenvalues; Eigenstates; Atomic structure; Observables; Particles; Perturbation theory; Quantum mechanics; Schrödinger equation; Time. Created 15-Jun-19 Revised 03-Aug-20