PX3827.5 Quantum Physics of Atoms
Introductory description
The principles of quantum mechanics are applied to a range of phenomena in atomic physics including the operation of a laser. The intrinsic property of spin is described and its relation to the indistinguishability of identical particles in quantum mechanics discussed. Perturbation theory and variational methods are described and illustrated for several examples. The hydrogen and helium atoms are analysed and the ideas that come out from this work are used to obtain a qualitative understanding of the periodic table.
Module aims
To develop the ideas of quantum theory and apply these to atomic physics
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.
Revision of 2nd year quantum theory

Approximation methods in quantum mechanics. Timeindependent perturbation theory, nondegenerate case, ground state of helium atom, degenerate case, Stark effect in hydrogen. Variational methods: Rayleigh  Ritz, ground state of helium atom

Spinorbit coupling and the Zeeman effect. Effects of spinorbit coupling, and the strong and weak field Zeeman effect using timeindependent perturbation theory

Many electron effectsindistinguishability of identical particles. Identical particles and spin; symmetric and antisymmetric states; discussion of periodic table, ionisation energies

Timedependent perturbation theory and the lasers. Derivation of Fermi's golden rule; radiation from atoms.; operation of the laser including stimulated emission and population inversion
Learning outcomes
By the end of the module, students should be able to:
 Use the approximate methods of quantum theory – perturbation theory (timedependent and timeindependent), variational methods
 Explain the role of spin and the Pauli exclusion principle
 Explain atomic spectra and the structure of the periodic table
 Describe the operation lasers
Indicative reading list
F Mandl, Quantum Mechanics, Wiley;
A.I.M. Rae, Quantum Mechanics, IOP, 2002;
S. Gasiorowicz, Quantum Physics, Wiley, 2003;
S.M. McMurry, Quantum Mechanics, AddisonWesley 1994
View reading list on Talis Aspire
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  13 sessions of 1 hour (17%) 
Other activity  2 hours (3%) 
Private study  60 hours (80%) 
Total  75 hours 
Private study description
Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers
Other activity description
2 problem classes
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D1
Weighting  Study time  

Coursework  15%  
Tests 

2 hour online examination (April)  85%  
Answer 2 questions from 3

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:
 Year 3 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 3 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 3 of UPXAF304 Undergraduate Physics (BSc MPhys)
 Year 3 of UPXAF300 Undergraduate Physics (BSc)
 Year 3 of UPXAF303 Undergraduate Physics (MPhys)
 Year 4 of UPXAF301 Undergraduate Physics (with Intercalated Year)
This module is Option list B for:

UMAAG105 Undergraduate Master of Mathematics (with Intercalated Year)
 Year 3 of G105 Mathematics (MMath) with Intercalated Year
 Year 5 of G105 Mathematics (MMath) with Intercalated Year
 Year 3 of UMAAG100 Undergraduate Mathematics (BSc)

UMAAG103 Undergraduate Mathematics (MMath)
 Year 3 of G103 Mathematics (MMath)
 Year 4 of G103 Mathematics (MMath)

UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 3 of G106 Mathematics (MMath) with Study in Europe
 Year 4 of G106 Mathematics (MMath) with Study in Europe
 Year 3 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 4 of UPXAGF14 Undergraduate Mathematics and Physics (with Intercalated Year)
 Year 4 of UMAAG101 Undergraduate Mathematics with Intercalated Year