Introductory description

This module explains how classical physics is unable to explain the properties of light, electrons and atoms. (Theories in physics, which make no reference to quantum theory, are usually called classical theories.) It covers the most important contributions to the development of quantum theory including: wave-particle 'duality', de Broglie's relation and the Schrodinger equation. The second half looks at applications of quantum theory to describe elementary particles: their classification by symmetry and how this allows us to interpret simple reactions between particles.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Waves, particles and thermodynamics before quantum theory

Light:
Thermal radiation and the origin of quantum theory: blackbody radiation, derivation for the case of a `1D black-body', Planck's hypothesis and E=hf . The photoelectric effect - Einstein's interpretation. The Compton effect - direct evidence for the particle nature of radiation.

Matter:
Atoms and atomic spectra a problem for classical mechanics. Bohr's Model of the Atom: quantisation of angular momentum, atomic levels in hydrogen. De Broglie's hypothesis.

Quantum Mechanics:
Correspondence Principle. The Schrödinger wave equation. Relation of the wave function to probability density. Probability distribution, need for normalisation. Superpositions of waves to give standing waves, beats and wave packets. Gaussian wave packet. Use of wave packets to represent localised particles. Group velocity and correspondence principle. Wave-particle duality, Heisenberg's uncertainty principle and its use to make order of magnitude estimates.

Using Schrödinger's equation:
Including the effect of a potential. Stationary states and the time-independent Schrödinger equation. Infinite potential well and energy quantisation. The potential step and the notion of tunnelling. Alpha decay of nuclei.

Principles of Elementary Particle Physics:
Simplicity, Composition, Symmetry, Unification. Quarks and Leptons as basic building blocks: Periodic Table of Quarks and Leptons; Basic composition rules for hadrons. The four forces and their roles: Electromagnetism, Gravity, Strong nuclear force, Weak nuclear force.

Observation and Experiment:
Natural radioactivity, source of geothermal energy, cosmic rays, natural
sources of neutrinos: radioactivity, solar, atmospheric. Charged particles in electric and magnetic fields, e/m for an electron, mass spectrometry, cathode ray tube, particle accelerators. Interactions of particles with matter: Ionisation, Pair creation by photons and Bremsstrahlung, hadronic interactions, probability of interaction: radiation and interaction lengths, particle detectors

The "big questions":
Origin of mass and the Higgs, Grand Unification as a goal, neutrino character and mass

Learning outcomes

By the end of the module, students should be able to:

• Discuss how experimental evidence implied a wave-particle duality for both light and matter
• Discuss the background to and issues surrounding Schrödinger's equation and its solutions
• Work with the time-independent Schrödinger equation for simple 1-dimensional potentials
• Classify the elementary particles giving the correct quantum number assignments to quark and lepton flavours
• Discuss the relationship between symmetries and conservation laws
• Explain the principles of experimental study of elementary particle physics
• Characterise natural radioactivity, cosmic rays, solar and atmospheric neutrinos

Indicative reading list

H. D. Young and R A Freedman, University Physics, Pearson

View reading list on Talis Aspire

Interdisciplinary

Quantum theory has been a joint endeavour between mathematics and physics since its inception. Particle physics is one of the success stories of this interdisciplinary collaboration - the Standard Model of particle physics is heavily based on concepts from algebra and differential geometry.

Quantum theory has applications beyond physics and mathematics. It is important in chemistry and increasingly computer science (quantum computing). One of the founders of the subject, Dirac, was a great interdisciplinarian. He trained as an engineer and is celebrated for his contributions to both mathematics and to physics.

This module is taken by many students from within Mathematical Sciences (mainly Mathematics and Physics).

Subject specific skills

Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.

Transferable skills

Analytical, communication, problem-solving, self-study