Quantum fluids are fluids, indeed. We have seen in the previous chapter what it means from a classical physics point of view. But quantum fluids are by definition ruled by quantum physics, as well. The goal of this chapter is to introduce some key concepts of quantum physics necessary to understand what makes a fluid a quantum one or rather what quantum property makes an ensemble of particles a quantum fluid. We are here precisely at the edge of our basic intuition of quantum physics. Indeed, one usually associates the notion of quantum object to a microscopic nature and it may thus a priori seem paradoxical to link the word quantum to a macroscopic object, such as the notion of fluid. Thinking it over a bit deeper, quantum physics is certainly present at all scales and we are confronted with quantum mechanics through the many electronic devices which have invaded our everyday life. And it actually turns out that, as we will see later on, most of these quantum devices are directly connected to the notion of quantum fluids, the case of electron fluids being certainly the most common one in such devices. Quantum physics has for sure deeply modified our everyday life. But it has also changed our perception of the world, and as we shall see in this chapter, it is precisely this new vision of the world which allows us to understand the concept of quantum fluids underlying so many physical systems.
Quantum fluids are fluids, indeed. We have seen in the previous chapter what it means from a classical physics point of view. But quantum fluids are by definition ruled by quantum physics, as well. The goal of this chapter is to introduce some key concepts of quantum physics necessary to understand what makes a fluid a quantum one or rather what quantum property makes an ensemble of particles a quantum fluid. We are here precisely at the edge of our basic intuition of quantum physics. Indeed, one usually associates the notion of quantum object to a microscopic nature and it may thus a priori seem paradoxical to link the word quantum to a macroscopic object, such as the notion of fluid. Thinking it over a bit deeper, quantum physics is certainly present at all scales and we are confronted with quantum mechanics through the many electronic devices which have invaded our everyday life. And it actually turns out that, as we will see later on, most of these quantum devices are directly connected to the notion of quantum fluids, the case of electron fluids being certainly the most common one in such devices. Quantum physics has for sure deeply modified our everyday life. But it has also changed our perception of the world, and as we shall see in this chapter, it is precisely this new vision of the world which allows us to understand the concept of quantum fluids underlying so many physical systems.
This is the third of three chapters that apply the concepts of Chapters 1, 2, and 3 to the three principal types of waves: mechanical, electromagnetic, and quantum. Although mechanical waves may be the most obvious in everyday life, and electromagnetic waves may be the most useful to our technological society, a case can be made that quantum waves are the most fundamental. As you'll see in this chapter, every bit of matter in the Universe behaves like a wave under certain circumstances, so it's hard to imagine anything more fundamental. If you're thinking that life in the macroscopic world moves along just fine without considering quantum effects, you should realize that the laws of classical physics are approximations, and all the quantum weirdness described in this chapter blends smoothly with classical physics when they overlap. Much of that weirdness comes from the dual wave and particle nature of matter and energy, and one of the goals of this chapter is to help you understand what's actually doing all this waving. This chapter begins with a comparison of the characteristics of waves and particles in Section 6.1, followed by a discussion of wave–particle duality in Section 6.2. You can read about the Schrödinger equation and probability wavefunctions in Sections 6.3 and 6.4, and quantum wave packets are discussed in Section 6.5. Wave and particle characteristics Before studying modern physics, most students think of particles and waves as belonging to fundamentally different categories of objects. That's understandable, because particles and waves have several very different characteristics, including the way in which they occupy space, the way they travel through openings, and the way they interact with other particles or waves. Here's a summary of some of the differentiating characteristics between particles and waves. Occupying space. Particles exist in a well-defined amount of space; if you could pause time at some instant during a tennis match, all of the spectators would agree on the position of the ball at that instant.
There is no dissent regarding the quantum theory success on the small-scale structure of the world but there is equally an open subject of debate about its interpretation. Both quantum mechanics and the theory of relativity are indeed extensions of classical mechanics, that is, they reproduce their results in other appropriate limiting cases. Quantum mechanics provides a new set of laws and a method of description of microscopic systems that has been very successful. The chapter discusses some of the fundamental principles of this highly controversial subject. In quantum physics, it is difficult to uphold a sharp distinction between the object and the observer. The chapter examines why quantum mechanics seems to be so hard for newcomers to learn and understand. The theory of quantum mechanics has led to many applications: laser, the electron microscope and many other technological devices.
This introductory chapter provides an overview of quantum mechanics, which is a subject of central importance in chemistry, and is by nature a mathematical theory. The chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of constituent molecules. However, at the microscopic level, atoms, molecules, and their constituent particles do not obey the familiar laws of mechanics that pertain to the everyday macroscopic world. For example, the existence of molecular line spectra indicates that molecules can be found only at certain well-defined energies, unlike objects at our own scale whose energy appears to be continuously variable. This book aims to explain the fundamentals of quantum mechanics from the point of view of chemistry; describe the areas of chemistry where quantum mechanics is most important; and show how quantum mechanics is applied to chemical problems.
The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.
Quantum mechanics forms the basis of modern physics. In a sense it is the parent theory about which we construct our view of the physical world. Briefly, quantum mechanics is the theory by which we describe the behaviors of subatomic and atomic particles, such as electrons, of which the macroscopic world is made. Although it is not necessary to treat macroscopic objects by use of quantum mechanics, the laws of quantum mechanics and their implications are completely consistent with Newton's Laws of Motion, which we know are applicable to most macroscopic objects. As we will see below, Newton's Laws of Motion are a special subset of quantum mechanics; quantum mechanics reduces to Newton's Laws at macroscopic dimensions. Before we begin our study of quantum mechanics, it is of interest to explain why quantum mechanics is of importance in the study of modern electrical engineering. Many new areas of electrical engineering are based on developments that can be understood only through the use of quantum mechanics. Among these are the broad areas of semiconductors and solid-state electronic devices, electro-optics and lasers, superconductors. It would be fair to say that in the study of each of the above areas some knowledge of quantum mechanics is essential. In this book, some basic concepts in quantum mechanics are presented that are necessary in the study of the above-mentioned disciplines. Introduction The concept most basic toward the understanding of quantum mechanics is the concept of measurement.
1.1 Waves and particles in quantum mechanics In spite of the fact that the extraordinary progress of experimental techniques make us able to manipulate at will systems made of any small and well defined number of atoms, electrons and photons making therefore possible the actual performance of the gedankenexperimente that Einstein and Bohr had imagined to support their opposite views on the physical properties of the wavelike/particlelike objects (quantons) of the quantum world it does not seem that, after more than eighty years, a unanimous consensus has been reached in the physicist's community on how to understand their strange properties. Unfortunately, we cannot know whether Feynman would still insist in maintaining his famous sentence It is fair to say that nobody understands quantum mechanics. We can only discuss if, almost thirty years after his death, some progress towards this goal has been made. I believe that this is the case. I will show in fact that, by following the suggestions of Feynman himself, some clarification of the old puzzles can be achieved. This chapter therefore by no means is intended to provide an impartial review of the present status of the question but is focused on the exposure of the results of more than twenty years of research of my group in Rome, which in my opinion provide a possible way of connecting together at the same time the random nature of the events at the atomic level of reality and the completeness of their probabilistic representation by the principles of Quantum Mechanics.