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 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.

The eyes of the world will be on London tonight as the opening ceremony will mark the start of the London 2012 Olympic Games. The ceremony will feature the largest harmonically tuned bell in Europe, there'll be NHS dancers, the Queen will be there too of course, and the grand finale will be the Olympic torch lighting the cauldron. While London has been gearing up for these momentous events, we here at Plus have been busy too.

The Plus team's vehicle of choice is the bicycle, so we're particularly pleased about an announcement that hit the news this month: a clever car mirror that eliminates the dreaded blind spot has been given a patent in the US. The mirror was designed by the mathematician Andrew Hicks, of Drexel University, after years of puzzling over the problem.

Why are we so clever? In evolutionary terms this isn't obvious: evolution tends to favour cheap solutions and the human brain is expensive. It consumes about 20% of our body's energy budget yet it only makes up 2% of our body mass. So why did it make evolutionary sense for us humans to develop powerful brains? Game theory provides a possible answer.

The holy grail for 21st century physics is to produce a unified theory of everything that can describe the world at every level, from the tiniest particles to the largest galaxies. Currently the strongest contender for such a theory is something called M-theory. So what is this supposed mother of all theories all about?

This year's Abel Prize goes to Endre Szemerédi for his "fundamental contributions to discrete mathematics and theoretical computer science."

Africa isn't a continent that's famous for cutting edge research. But at the University of Stellenbosch, 50km East of Cape Town, South Africa, Kiran Dellimore and his team are engineering medical equipment that will save the lives of people all over the world. Latest projects include replacement heart valves made from kangaroo tissue and equipment to help resuscitate people in emergencies.