London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.

In the 1920s the Austrian physicist Erwin Schrödinger came up with what has become the central equation of quantum mechanics. It tells you all there is to know about a quantum physical system and it also predicts famous quantum weirdnesses such as superposition and quantum entanglement. In this, the first article of a three-part series, we introduce Schrödinger's equation and put it in its historical context.

In the previous article we introduced Schrödinger's equation and its solution, the wave function, which contains all the information there is to know about a quantum system. Now it's time to see the equation in action, using a very simple physical system as an example. We'll also look at another weird phenomenon called quantum tunneling.

In the first article of this series we introduced Schrödinger's equation and in the second we saw it in action using a simple example. But how should we interpret its solution, the wave function? What does it tell us about the physical world?

Predicting the final Olympic medal count is a black art. Sport, with all its intricacies and vagaries, is always susceptible to variations in form, weather conditions and simple random events. But we like a challenge! So without further ado, here is our predicted 2012 London Olympic medal count.

In our article Mapping the medals we came up with our very own prediction of the 2012 Olympic medal counts for the top 20 countries! This interactive map tells you how our predictions stack up: click on a country to see its actual medal count, our prediction and the results from 2008.