Module description
This module introduces the quantum description of matter and radiation. The theoretical and experimental background to the de Broglie equations is summarised and from these relationships the time-dependent and time-independent Schrodinger equations are obtained. The wave-functions which provide solutions to these equations are interpreted. Schrodinger's equation is applied to a particle in a box, a simple harmonic oscillator, scattering by a potential well and the penetration of a potential barrier. The two-particle problem is used to introduce the concept of parity. The full quantum solution of the hydrogen atom is then derived.

Learning outcomes
After taking this module students should be able to:

• appreciate the difficulty in understanding matter on the small scale in terms of everyday concepts
• follow the basic ideas that lead to Schrodinger's equation
• recognise the success of Schrodinger's equation in explaining discrete bound state, insulators, semi-conductors and conductors, scattering and tunnelling
• understand the quantum solution of the hydrogen atom
• appreciate the concept of spin in understanding magnetic properties

Outline syllabus
Recap of wave-particle duality.
De Broglie relationships and Schrodinger's equation.
Operators, dynamical variables and possible results of a measurement. Expectation values.
Solution of Schrodinger's equation for an infinite well.
Degeneracy. Correspondence Principle. Symmetric and anti-symmetric solution.
Zero-point energy and specific heat at low temperatures. Uncertainty Principle.
Potential well with ion lattice. Symmetry argument for valence and conduction bands. Insulators, conductors and semi-conductors.
Symmetric and anti-symmetric solution. Bosons and Fermions.
Scattering by a finite well and Ramsauer effect.
Barrier penetration (approximate solution). Field-emission microscope and scanning microscope. Alpha-decay.
Quantum representation of angular momentum.
Hydrogen atom.
Spin, magnetism and NMR.