Aims

The aim of the module is to understand simple quantum systems with bound states and learn methods to solve the Schrodinger equation approximately.

Learning objectives

At the end of the module you should be able to:

• understand basic properties of spherical harmonics;
• understand the quantum harmonic oscillator and hydrogen atom;
• use time-independent perturbation theory to find approximate solutions when the exact solutions cannot be found;

Syllabus

• One-dimensonal Schrodinger equation with bound states: particle in a square-well potential (if time permits) and the harmonic oscillator
• One-dimensional quantum scattering problem (if time permits)
• Three-dimensional Schrodinger equation with a central potential: spherical harmonics
• The quantum hydrogen atom
• Time-independent perturbation theory for the Schrodinger equation.

Recommended texts

• S Gasiorowicz, Quantum Physics (2nd edn), Wiley (UJ 0.12 GAS)
• A Sudbery, Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians, Cambridge University Press (out of print) (U 0.12 SUD)

Teaching

• Summer Term
• 4 lectures per week
• 1 problems/seminar class per week

Assessment

One and a half hour closed examination towards the end of the Summer Term (90%),
Coursework (10%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

This module is not available as an elective.

Prerequisites

• all Taught in: Vector Calculus II 
• all Taught in: Differential Equations 
• all Taught in: Analytical Mechanics 
• all Taught in: Electromagnetism
• all Taught in: Quantum Mechanics
• all Taught in: Integral Transforms
• all Taught in: Vibrations and Waves  (desirable but not necessary)