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# Field Theory

Structure Type: Study unit IX00BE88 TT 2023 Bachelor of Engineering 4 (2026-2027) Autumn 5 cr Mäkelä, Jarmo Finnish

Taking the course in advance? See the courses during the academic year 2023-2024.

## Learning Outcomes

In this course we shall learn to apply the mathematical skills learned in the Real Analysis and Complex Analysis courses in the solutions of physical problems. The central topic of the course is the theory of the electromagnetic fields, which is based on Maxwell’s equations. In the same way as classical mechanics as a whole may be derived from Newton’s three law of motion, the general theory of electromagnetism, at least as far as we limit our considerations to the electric and the magnetic fields alone, may be derived from Maxwell’s equations. Actually, almost all modern technology is based on Maxwell’s equations. In this course the student learns to determine the properties of the electric, and magnetic fields by means of solving Maxwell’s equations. In addition, we shall consider briefly the so-called Schrödinger equation, which is the basis of the atomic-, and nuclear physics, together with its solutions and properties.

## Contents

1) A brief summary of vector analysis,
2) Maxwell’s equations,
3) Static electric fields,
4) Static magnetic fields,
5) Slowly varying fields,
6) Fast varying fields: Electromagnetic waves,
7) Elements of quantum physics: Photons, wave-particle dualism and uncertainty principle,
8) The Schrödinger equation,
9) Particle in a potential box,
10) Tunneling,
11) Harmonic oscillator,
12) Hydrogen atom.
13) Many-electron atoms,
14) Molecules and solids,
15) Elements of nuclear physics.

## Recommended or Required Reading and Other Learning Resources/Tools

Suggested Reading: L. Solymar: Lectures on electromagnetic theory (Oxford University Press).