Over the past hundred years or so, physicists have developed a foolproof and powerful tool that allows us to understand everything and anything in the universe. You take the object that you’re interested in and you throw something at it. Ideally, you throw something at it really hard. This technique was developed around the turn of the 20th century and has since allowed us to understand everything from the structure of atoms, to the structure of materials, to the structure of DNA. In short, throwing stuff at other stuff is the single most important experi- mental method available to science. Because of this, it is given a respectable sounding name. We call it scattering.

This chapter explores what we could do with a computer whose operating system is quantum mechanics, rather than classical mechanics. One of the answers is: factorise primes really quickly. We will explain why this is interesting.

We all know what a wave is. But you may not know just how many different kinds of waves there are and what strange and interesting properties they have. We start this chapter with something very familiar from everyday life: waves on the surface of an ocean. While they may be familiar, their mathematical description is surprisingly subtle. This can be traced, like so many other things in fluid mechanics, to the boundary conditions.

The fundamentals of electromagnetism are simple. Moving electric charges set up electric and magnetic fields. In turn, these fields make the charges move. This dance between charges and fields is described by the Maxwell equations. This brief chapter describes how this comes about. It is, in a sense, everything you need to know about electromagnetism, enshrined in these simple equations. The rest of the book is mere commentary.

The laws of classical mechanics are valid in so-called inertial frames. Roughly speaking, these are frames that are at rest. But what if you, one day, find yourself in a frame that is not in- ertial? For example, suppose that every 24 hours you happen to spin around an axis which is 2500 miles away. What would you feel? Or what if every year you spin around an axis 36 million miles away? Would that have any effect on your everyday life? In this chapter, we describe what happens if you sit in a rotating reference frame and the effects of the resulting centrifugal and Coriolis forces.

To understand what the Maxwell equations are telling us, it’s useful to dissect them piece by piece. The simplest piece comes from looking at stationary electric charges and how they give rise to electric fields. A consequence of this is the Coulomb force law between charges. This, and much more, will be described in this chapter.

The chapter then goes on to explore many other different kinds of waves that arise in different situations, from the atmosphere, to supersonic aircraft to traffic jams.

Theres a lot of interesting physics to be found if you subject an atom to an electric or magnetic field. This chapter explores this physics. It covers the Stark effect and the Zeeman effect and Rabi oscillations. it also looks at what happens when coherent states of photons in a cavity interact with atoms.

In this chapter, we ease in gradually by thinking about a quantum particle moving along a line. This provides an opportunity for us to learn about the properties of the wavefuntion and how it encodes properties such as the position and momentum of the particle. We will also see how the physics of a system is described by the Schrodinger equation.

A qubit is the classical version of a bit in the sense that it can take one of two values. But the key idea of the quantum world is that it can, in fact, take both values at the same time. Here we explore the physics of the qubit and use it as a vehicle to better understand some of the stranger features of quantum mechanics.

When a quantum system has some external time dependence, some rather special things happen. This chapter explores this subject. Among the topics that we cover are the adiabatic theorem, Berry phase, the sudden approximation, and time-dependent perturbation theory.

There are two great equations of classical physics: one is Einstein’s equation of general relativity, the other the Navier-Stokes equation that describes how fluids flow. In this chapter, we meet Navier-Stokes.

This equation differs from the Euler equation by the addition of a viscosity term. This is not a small change and makes solutions to the Navier-Stokes equation much richer and more subtle than those of the Euler equation. In this chapter, we begin our exploration of these solutions.

There are two great post-Newtonian steps in classical mechanics. The first is the Lagrangian formulation and the accompanying principle of least action. The second is the Hamiltonian formulation, which is yet another way of writing Newtons equation of motion that uncovers what is really going on. This is where we start to see the deep and beautiful mathematical structure that underlies classical mechanics. It is also where we can make connections to what comes next, with quantum mechanics following very naturally from the Hamiltonian formulation.