Preface in Delft,where both research and education rather concentrate on down-to-earth topics. ntum dots.super ronics,and ma others.The theoretical part of the curriculum is designed to support this research in the most efficient way:after a solid treatment of the basics,the emphasis is quickly shifted to apply the theory to understand the essential properties of quantum devices.This book is written with the same philosophy.It presents the fundamentals of advanced quantum theory at an operational level:we have tried to keep the technical and mathematical basis as simple as pos sible,and as soon as we have enough theoretical tools at hand we move on and give examples how to use them. The book starts with an introductory chapter on basic quantum mechanics.Since this book is intended for a course on advanced quantum mechanics.we assume that the reader is already familiar with all concepts discussed in this chapter.The reason we included it was to make the book more"self-contained."s well as tom ake sure that we all understand the basics in the same way when we discuss advanced topics.The following two chapters introduce new material:we extend the basic quantum theory to describe many (identical) particles,instead of just one or two,and we show how this description fits conveniently in the framework of second quantization. then have all the to effects in many-particle the cd part(Chapter)epro vide some examples and show how we can understand magnetism,superconductivity,and superfluidity by straightforward use of the theoretical toolbox presented in the previous chapters. After focusing exclusively particle quantum theory in the first parts of the book.we then m ve on to in into our theoretical fra work.In Chapters and 8 we explain in very general terms how almost any classical field can be"quantized and how this procedure naturally leads to a very particle-like treatment of the excitations of the fields.We give many examples,but keep an emphasis on the electromagnetic field because of its fundamental importance.In Chapter 9 we then provide the last"missing epuzzle":we explain how to describe the interaction between particles and efield.With this knowledge at hand,we construct simple models t describe several phenomena from the field of quantum optics:we discuss the radiative decay of excited atomic states,as well as Cherenkov radiation and Bremsstrahlung,and we give a simplified picture of how a laser works.This third part is concluded with a short introduction on coherent states:a very general concept,but in particular very important in he field of quantu optic In the fourth part of the book follows anique master-level introduction to dissipativ quantum mechanics.This field developed relatively recently (in the last three decades) and is usually not discussed in textbooks on quantum mechanics.In practice,however,the concept of dissipation is as important in quantum mechanics as it is in classical mechanics The idea of a e.g.a harn onic oscillator which is brought into a station ary excited eigenstate and will stay there forever,is in reality too idealized interaction with a(possibly very complicated)environment can dissipate energy from the system and can ultimately bring it to its ground state.Although the problem seems inconceivably hardxii Preface in Delft, where both research and education rather concentrate on down-to-earth topics. The DUT is one of the world-leading centers doing research on quantum devices such as semiconductor quantum dots, superconducting qubits, molecular electronics, and many others. The theoretical part of the curriculum is designed to support this research in the most efficient way: after a solid treatment of the basics, the emphasis is quickly shifted to apply the theory to understand the essential properties of quantum devices. This book is written with the same philosophy. It presents the fundamentals of advanced quantum theory at an operational level: we have tried to keep the technical and mathematical basis as simple as possible, and as soon as we have enough theoretical tools at hand we move on and give examples how to use them. The book starts with an introductory chapter on basic quantum mechanics. Since this book is intended for a course on advanced quantum mechanics, we assume that the reader is already familiar with all concepts discussed in this chapter. The reason we included it was to make the book more “self-contained,” as well as to make sure that we all understand the basics in the same way when we discuss advanced topics. The following two chapters introduce new material: we extend the basic quantum theory to describe many (identical) particles, instead of just one or two, and we show how this description fits conveniently in the framework of second quantization. We then have all the tools at our disposal to construct simple models for quantum effects in many-particle systems. In the second part of the book (Chapters 4–6), we pro￾vide some examples and show how we can understand magnetism, superconductivity, and superfluidity by straightforward use of the theoretical toolbox presented in the previous chapters. After focusing exclusively on many-particle quantum theory in the first parts of the book, we then move on to include fields into our theoretical framework. In Chapters 7 and 8, we explain in very general terms how almost any classical field can be “quantized” and how this procedure naturally leads to a very particle-like treatment of the excitations of the fields. We give many examples, but keep an emphasis on the electromagnetic field because of its fundamental importance. In Chapter 9 we then provide the last “missing piece of the puzzle”: we explain how to describe the interaction between particles and the electromagnetic field. With this knowledge at hand, we construct simple models to describe several phenomena from the field of quantum optics: we discuss the radiative decay of excited atomic states, as well as Cherenkov radiation and Bremsstrahlung, and we give a simplified picture of how a laser works. This third part is concluded with a short introduction on coherent states: a very general concept, but in particular very important in the field of quantum optics. In the fourth part of the book follows a unique master-level introduction to dissipative quantum mechanics. This field developed relatively recently (in the last three decades), and is usually not discussed in textbooks on quantum mechanics. In practice, however, the concept of dissipation is as important in quantum mechanics as it is in classical mechanics. The idea of a quantum system, e.g. a harmonic oscillator, which is brought into a station￾ary excited eigenstate and will stay there forever, is in reality too idealized: interactions with a (possibly very complicated) environment can dissipate energy from the system and can ultimately bring it to its ground state. Although the problem seems inconceivably hard