## Articles

Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi. Yet, the puzzle holds fascination in both fields.

Ocean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths.

Space is three-dimensional... or is it? In fact, we are all used to living in a curved, multidimensional universe. And a mathematical argument might just explain how those higher dimensions are hidden from view.

String theory has one very unique consequence that no other theory of physics before has had: it predicts the number of dimensions of space-time. But where are these other dimensions hiding and will we ever observe them?

Andy Murray and Laura Robson made a good team at London 2012, bringing home silver in the mixed doubles. But how do you make sure that the competing pair is the best you can pick from the team?

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.