This chapter explores the patterns of electron probability waves around atoms, called orbitals, and the way they spread out to encompass groups of atoms to make molecules, and spread out even further to become the conduction bands in metals that allow electrons to flow freely. It shows standing waves, from optical standing waves created when laser light is reflected back on itself, to sound waves in metal plates, to probability waves for electrons in hydrogen, and one created when electrons reflect off atoms in a metal surface. The physics of atoms allows the reader to understand how the world works. The Pauli exclusion principle explains the structure of atoms and, astonishingly, also explains white dwarf stars and neutron stars. The world of atoms and solids is the world around the reader, but the tiny size of atoms and quantum rules that they obey is normally considered beyond the reach of school science.
This chapter explores the patterns of electron probability waves around atoms, called orbitals, and the way they spread out to encompass groups of atoms to make molecules, and spread out even further to become the conduction bands in metals that allow electrons to flow freely. It shows standing waves, from optical standing waves created when laser light is reflected back on itself, to sound waves in metal plates, to probability waves for electrons in hydrogen, and one created when electrons reflect off atoms in a metal surface. The physics of atoms allows the reader to understand how the world works. The Pauli exclusion principle explains the structure of atoms and, astonishingly, also explains white dwarf stars and neutron stars. The world of atoms and solids is the world around the reader, but the tiny size of atoms and quantum rules that they obey is normally considered beyond the reach of school science.
The electric field intensity of a standing-wave laser field is periodic in space. Due to the ac Stark effect, this gives rise to a spatially periodic potential acting on an atom, as explained in Chapter 4 (see, e.g., Eq. (4.31)). This is the physical principle behind the generation of optical lattices. By superimposing a number of different laser beams it is possible to generate potentials which are periodic in one, two or three dimensions. The suggestion that standing light waves may be used to confine the motion of atoms dates back to 1968 and is due to Letokhov. The first experimental realization of an optical lattice was achieved in 1987 for a classical gas of cesium atoms. The study of atoms in such potentials has many different facets. At the simplest level, it is possible to study the energy band structure of atoms moving in these potentials and to explore experimentally a number of effects that are difficult to observe for electrons in the periodic lattice of a solid. Interactions between atoms introduce qualitatively new effects. Within mean-field theory, which applies when the number of atoms in the vicinity of a single minimum of the potential is sufficiently large, one finds that interatomic interactions give rise to novel features in the band structure. These include multivaluedness of the energy for a given band and states possessing a periodicity different from that of the optical lattice.
Abstract Surfing the Quantum World bridges the gap between in-depth textbooks and typical popular science books on quantum ideas and phenomena. Among its significant features is the description of a host of mind-bending phenomena, such as a quantum object being in two places at once or a certain minus sign being the most consequential in the universe. Much of its first part is historical, starting with the ancient Greeks and their concepts of light, and ending with the creation of quantum mechanics. The second part begins by applying quantum mechanics and its probability nature to a pedagogical system, the one-dimensional box, an analog of which is a musical-instrument string. This is followed by a gentle introduction to the fundamental principles of quantum theory, whose core concepts and symbolic representations are the foundation for most of the subsequent chapters. For instance, it is shown how quantum theory explains the properties of the hydrogen atom and, via quantum spin and Pauli’s Exclusion Principle, how it accounts for the structure of the periodic table. White dwarf and neutron stars are seen to be gigantic quantum objects, while the maximum height of mountains is shown to have a quantum basis. Among the many other topics considered are a variety of interference phenomena, those that display the wave properties of particles like electrons and photons, and even of large molecules. The book concludes with a wide-ranging discussion of interpretational and philosophic issues, introduced in Chapters 14 by entanglement and 15 by Schrödinger’s cat.
Most scientists immediately associate optics with photons. Indeed optics, defined as the study of the properties of light, is one of the oldest fields of physics – dating back to the earliest civilisations – and is still a thriving area of research. But there is more to optics than light and lasers. “Matter wave” optics, where electrons and neutrons take the place of photons, began with the demonstration of the wave nature of the electron by G P Thomson, Davisson and Germer n the 1920s. Since then electron and neutron interferometers have been used in many beautiful experiments that have improved our understanding of quantum mechanics. Beams of electrons and neutrons have also become indispensable tools in the study of solids and surfaces. Therefore it was perhaps inevitable that one day physicists would be able to do optics with atoms – to coherently split, focus and refract beams of neutral atoms.
Quantum mechanics is a theory to explain and predict the behavior of particles such as electrons, protons, neutrons, atomic nuclei, atoms, and molecules, as well as the photon–the particle associated with electromagnetic radiation or light. From quantum theory we obtain the laws of chemistry as well as explanations for the properties of materials, such as crystals, semiconductors, superconductors, and superfluids. Applications of quantum behavior give us transistors, computer chips, lasers, and masers. The relatively new field of molecular biology, which leads to our better understanding of biological structures and life processes, derives from quantum considerations. Thus, quantum behavior encompasses a large fraction of modern science and technology. Quantum theory was developed during the first half of the twentieth century through the efforts of many scientists. In 1926, E. Schrödinger interjected wave mechanics into the array of ideas, equations, explanations, and theories that were prevalent at the time to explain the growing accumulation of observations of quantum phenomena. His theory introduced the wave function and the differential wave equation that it obeys. Schrödinger's wave mechanics is now the backbone of our current conceptional understanding and our mathematical procedures for the study of quantum phenomena. Our presentation of the basic principles of quantum mechanics is contained in the first three chapters. Chapter 1 begins with a treatment of plane waves and wave packets, which serves as background material for the subsequent discussion of the wave function for a free particle.
The identity and size of atoms is explicable only in quantum physics. The double slit experiment illustrates the wave-particle duality of light and of matter. To describe quantum interference the concept of a complex probability is introduced, the squared amplitude of which is the probability of a particle being at a particular location. The uncertainty relation requires atomic motion in solids even at absolute zero. The symmetry of exchanging indistinguishable particles leads to the classification of particles as fermions or bosons. The exclusion principle applies to electrons and rationalises the Periodic Table and much more. Electrons in solids exist in bands of energy. Band theory explains why some materials are electrical conductors, others are insulators or semiconductors. Chemical bonding involves quantum tunnelling of electrons. Hydrogen may diffuse in solids by quantum tunnelling. The temperature dependence of the specific heat of a solid is explicable only in quantum physics.
Chapter 3 provides a brief review of a few concepts from classical Newtonian physics, and how this fails to explain phenomena at the nanoscopic scale. As is detailed within, the classical mechanical model is able to describe all observed physical phenomena; however, when it comes to the nanoscale this model breaks down, because the properties of the materials change dramatically. At this scale, the surface-to-volume ratio increases, gravitational forces become negligible and random molecular motion becomes more important. This changes the properties of the material and affects the devices that are fabricated at this scale. It is hence necessary to develop a new model that can explain such physical phenomena. This has led to a new branch of physics, i.e. quantum physics (QP) or quantum mechanics, which is able to explain the behavior observed at nanoscale. QP enables us to explain phenomena such as the photoelectric effect, Compton effect. etc. In this chapter, we introduce quantum mechanics and how it evolved in the late 19th and early 20th centuries. Further, light’s behaviour as a particle as well as a wave is described by the photoelectric effect and Young’s double-slit experiment, respectively. Further, the dual nature of the particle is explained using the de Broglie principle. Schrodinger’s equation is then explained, which gives the probability of finding a subatomic-scale particle at a certain position in a quantum well. In addition to the formulation of Schrodinger’s equation, its solution, the concept of a potential well, the characteristics of the wave function and its interpretation and significance, and, finally, the application of Schrodinger’s equation in the structure of an atom form subsequent parts of this chapter. The equation serves as a basis with which to understand band theory. Band theory explains the difference between conductors, insulators and semiconductors. Materials are distinguished according to the differences in their band gaps. Adding impurities or varying temperature changes the band gap in semiconductors, which consequently changes the properties of the semiconductor and its electrical conduction. One more important measure to understand and exploit the properties and behaviour of materials is Fermi–Dirac statistics. It is useful to acquire the probability of electrons at a given energy level at a specific temperature. These concepts can be utilised by physicists and chip makers to make more energy-efficient devices. Hence, this chapter details the fundamentals of quantum physics and how they relate to the electrical properties of nanodevices.