PX1016 Quantum Phenomena
Introductory description
This module starts by explaining 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 then deals with the most important contributions to the development of quantum physics including those of: Planck, who first suggested that the energy in a light wave comes in discrete units or 'quanta'; Einstein, whose theory of the photoelectric effect implied a 'duality' between particles and waves; Bohr, who suggested a theory of the atom that assumed that not only energy but also angular momentum was quantised; and Schrödinger who wrote down the first waveequations to describe matter.
Module aims
The module should describe how the discovery of effects which could not be explained using classical physics led to the development of quantum theory. The module should develop the ideas of waveparticle duality and introduce the wave theory of matter based on Schrödinger's equation.
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 blackbody', the idea of modes, Wien's law, RayleighJeans formula, Planck's hypothesis and E=hf . The photoelectric effect  Einstein's interpretation.
Waves or Particles? Interference a problem for the particle picture; 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: quantization of angular momentum, atomic levels in hydrogen. De Broglie's hypothesis. Experimental verification of wavelike nature of electrons  electron diffraction
Quantum Mechanics:
Correspondence Principle. The Schrödinger wave equation. Relation of the wavefunction to probability density. Probability distribution, need for normalization. Superpositions of waves to give standing waves, beats and wavepackets. Gaussian wavepacket. Use of wavepackets to represent localized particles. Group velocity and correspondence principle again. Waveparticle duality, Heisenberg's uncertainty principle and its use to make order of magnitude estimates.
Using Schrödinger's equation:
Including the effect of a potential. Importance of stationary states and timeindependent Schrödinger equation. Infinite potential well and energy quantization. The potential step  notion of tunnelling. Alpha decay of nuclei. Status of wave mechanics.
Learning outcomes
By the end of the module, students should be able to:
 Discuss how key pieces of experimental evidence implied a waveparticle duality for both light and matter
 Discuss the background to and issues surrounding Schrödinger's equation. This includes the interpretation of the wave function and the role of wave packets and stationary states
 Manipulate the timeindependent Schrödinger equation for simple 1dimensional potentials
Indicative reading list
H. D. Yo.ung 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. It has applications to 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 both for his contributions to 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, problemsolving, selfstudy
Study time
Type  Required 

Lectures  15 sessions of 1 hour (25%) 
Private study  45 hours (75%) 
Total  60 hours 
Private study description
Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for the exam, practising on past exam papers
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group B1
Weighting  Study time  

2 hour online examination (Summer)  100%  
Answer 2 questions

Feedback on assessment
Meeting with personal tutor, group feedback
Courses
This module is Core for:
 Year 1 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 1 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 1 of UPXAF304 Undergraduate Physics (BSc MPhys)
 Year 1 of UPXAF300 Undergraduate Physics (BSc)
 Year 1 of UPXAF303 Undergraduate Physics (MPhys)
 Year 1 of UPXAF3N1 Undergraduate Physics and Business Studies
 Year 1 of UPXAF3F5 Undergraduate Physics with Astrophysics (BSc)
 Year 1 of UPXAF3FA Undergraduate Physics with Astrophysics (MPhys)
 Year 1 of UPXAF3N2 Undergraduate Physics with Business Studies
This module is Optional for:
 Year 1 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 1 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 1 of USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 1 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics
This module is Option list B for:
 Year 1 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 1 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 1 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 1 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 1 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 1 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 1 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
 Year 1 of UMAAGV18 Undergraduate Mathematics and Philosophy with Intercalated Year
 Year 1 of UMAAG101 Undergraduate Mathematics with Intercalated Year