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.

If youre going to understand one thing in physics then it should be the harmonic oscillator. It is simple system that underlies nearly everything else that we do. This chapter studies the quantum harmonic oscillator, solving it several times in different ways to highlight different features.

Our discussion in early chapters captures the spirit of quantum mechanics but is restricted to particles moving along a line. Thats not very unrealistic. In this chapter we breathe some life into quantum particles and allow them to roam in three-dimensional space. This entails an understanding of angular momentum. We will pay particular attention to the hydrogen atom, whose quantum solution was one of the first great triumphs of quantum mechanics and still underlies all of atomic physics.

The periodic table is one of the most iconic images in science. All elements are classified in groups, ranging from metals on the left that go bang when you drop them in water through to gases on the right that don’t do very much at all. The purpose of this chapter is to start to look at the periodic table from first principles, to understand the structure and patterns that lie there.

The purpose of this chapter is to understand how quantum particles react to magnetic fields. There are a number of reasons to do be interested in this. First, quantum particles do extraordinary things when subjected to magnetic fields, including forming exotic states of matter known as quantum Hall fluids. But, in addition, magnetic fields bring a number of new conceptual ideas to the table. Among other things, this is where we first start to see the richness that comes from combining quantum mechanics with the gauge fields of electromagnetism.

The difference between quantum and classical mechanics does not involve just a small tweak. Instead it is a root and branch overhaul of the entire framework. In this chapter we introduce the key concept that underlies this new framework: the quantum state, as manifested in the wavefunction.

Physicists have a dirty secret: we’re not very good at solving equations. More precisely, humans aren’t very good at solving equations. We know this because we have computers and they’re much better at solving things than we are. This means that we must develop a toolbox of methods so that, when confronted by a problem, we have some options on how to go about understanding whats going on. The purpose of this chapter is to develop this toolbox in the guise of various approximation schemes.

Symmetries are a key idea in physics. In the classical world, they are associated to conservation laws, courtesy of Emmy Noether. The same, and more, is true in the quantum world. In this chapter we explore how symmetries manifest themselves in quantum mechanics. Special attention will be given to time evolution and the role of SU(2) and angular momentum

Our goal in this chapter is to look more closely at the underlying mathematical formalism of quantum mechanics. We will look at the quantum state, how it evolves in time, and what it means to interrogate the state by performing a measurement. It is here that we meet the famed Heisenberg uncertainty principle.

Quantum particles, like happy families, are all the same. In fact, not only are they the same. They are literally indistinguishable. This has deep and important consequences that are fleshed out in this chapter.

What is the essence of quantum mechanics? What makes the quantum world truly different from the classical one? Is it the discrete spectrum of energy levels? Or the inherent lack of determinism? The purpose of this chapter is to go back to basics in an attempt to answer this question. We will look at the framework of quantum mechanics in an attempt to get a better understanding of what we mean by a “state”, and what we mean by a “measurement”. A large part of our focus will be on the power of quantum entanglement.