Chapter 14 is entirely devoted to the electron spin and an introduction to quantum entanglement. The first part deals with the groundbreaking discovery of spin, its introduction into quantum formalism, and some of its most important effects on atomic spectra, notably the anomalous Zeeman effect. Historically, spin has been considered as an angular momentum that particles can have by the mere fact of their existence, which is called "intrinsic" and does not require any explanation. To address this shortcoming, Section 4 presents a possible explanation for the origin of electron spin as a result of its interaction with the vacuum field. Section 5 introduces the entangled system of two particles with spin, which provides an opportunity to discuss, necessarily schematically, the Schrödinger cat and the Einstein-Podolsky-Rosen thought experiment, as well as the Bell inequalities.

Handed a spectrum, the work begins. In this chapter, we explain how one takes a spectrum and objectively locates and quantifies the statistically significant absorption features peppered throughout. We describe a continuum normalization method that is objective and provides an error model. Multiple spectra may be co-added to improve signal to noise. For objectively locating absorption features, we present a scanning algorithm weighted by the line spread function and optimized for weak lines. Multiple absorption lines arising in rich absorption systems can be found using autocorrelation methods, and one such method is described. To analyze absorption systems, a systemic absorber redshift is determined, and the wavelength scale of all absorption profiles is converted to and aligned in the absorber’s rest-frame velocity. For high-resolution profiles, methods are presented for measuring equivalent widths and quantifying kinematics directly from pixel flux decrements. These include velocity spreads containing 90% of total optical depth and other flux decrement weighted velocity moments. We conclude with detailed methods for building composite two-point velocity correlation functions.

Every recorded quasar spectrum is a blemished version of an otherwise pure light beam. It is blurred by the atmosphere and suffers interference and scattering when reflected off optical elements. It is imperfectly collimated, impurely dispersed, iteratively refocused, and inefficiently discretized when recorded. It is then converted to analog and re-digitized, which introduces “read” errors to an already noise-ridden Poissonian process of photon counting. To understand spectra, one needs to understand its recording device, the spectrograph. In this chapter, a range of long-slit low-resolution spectrographs and high-resolution echelle spectrographs are described. Grating equations, blaze functions, and cross dispersers are examined in detail. The equations for resolving power and instrumental resolution are derived from first principles, followed by illustrations showing the impact of CCD pixelization and line broadening on recorded absorption lines. We present quantitative models for the recorded counts in observed spectra. Flux calibration is also derived from first principles of telescope characteristics and spectrograph design. Finally, integrated field units are described.

Chapter 5 familiarizes the student with some of the most basic features of quantum systems, by applying the Schrödinger equation to simple, one-dimensional problems. It shows that it is possible to obtain qualitatively correct conclusions about the behavior of quantum particles in the presence of more or less arbitrary potentials by replacing them with piecewise-constant potentials, which greatly simplifies the mathematics. Replacing the real potential with a simpler one that retains its basic characteristics has the great advantage of allowing us to study the essence of the physical situation, as illustrated by the examples of the one-dimensional potential step, the square well, the square potential barrier and the symmetric double well. These examples are used to discuss specific features such as quantum tunneling, and applications such as masers and molecular clocks.

Galaxies do not live alone; they live in groups and clusters; they are surrounded by smaller companions bound in or passing through their dark matter halos. As such, there is some ambiguity when studying the CGM in connection to “isolated” galaxy properties because gas is shared between galaxies and companions. In this chapter, we describe halo occupation distribution (HOD) theory, which characterizes the average distribution of companions associated with a given galaxy. HOD relations guide our quantified definitions of galaxy groups and clusters and provide a formalism within which absorption line studies can be applied to the intragroup medium (IGrM) and the intracluster medium (ICM). The remainder of this chapter covers the characteristic properties of the IGrM and the ICM. The IGrM is primarily discussed in terms of theoretical hydrodynamic simulations of small groups like our own Local Group. Of interest are the dynamic “boundaries” between the individual CGM of the orbiting member galaxies and the common IGrM envelope. Mergers are briefly discussed followed by a detailed characterization of the ICM based on X-ray emission studies.

Empirically demonstrating the association of metal-line absorber lines with galaxies has a long, rich history from the earliest theoretical predictions in the mid 1960s to observational confirmation in the 1990s. From that point onward, quasar absorption line studies became a powerful tool for characterizing the gaseous halos of galaxies. Countless works have provided valuable insights into the chemical, ionization, and kinematic conditions of what is now called the circumgalactic medium. A new concept called the baryon cycle was birthed in which the balance of accretion modes, stellar feedback, gas recycling, and outflow dynamics of galactic gas was found to be closely linked to how baryons respond to dark matter halos of a given mass. Modern theory known as halo abundance matching has helped us empirically connect the average stellar mass to dark matter halos of a given mass. Powerful hydrodynamics simulations tell a story in which the average baryon cycle processes in a galaxy are closely linked to dark matter halo mass. In this chapter, we discuss how synthesizing both the observational data and theoretical insights has yielded a simple composite model of the baryon cycle.

Chapter 1 begins by introducing the quantum world as part of the physical world, not in opposition to or separate from the classical world. It then introduces the basic tools needed to work with quantum mechanics, and describes the scope and purpose of this textbook. It discusses how despite its successes, current quantum mechanics lacks adequate explanations for important observed atomic properties, suggesting an incompleteness of the theory. After a brief overview of its main interpretative issues , the chapter concludes with an introduction of the vacuum or zero-point field as the physical element that restores causality and serves to complete the quantum picture by providing a causal explanation of characteristic quantum phenomena.

The 1960s through the 1970s was an exciting era of the discovery of quasars. During this time the study of these cosmologically distant luminous sources developed into a powerful tool that changed the course of the science of astronomy. This story runs in parallel with technological advances in both light-gathering capability and computing power. In this chapter, we chart the development of the study of quasars and show how quasar absorption lines provide a tool for studying the properties of diffuse gas across the full dynamic range of astrophysical environment out to the highest redshifts.

The wave model of hydrogenic ions naturally yields transition probabilities. These probabilities are written in terms of three Einstein coefficients, which are determined from “overlap integrals” for spontaneous emission. Under the assumption that a simple dipole describes the moment between the charge densities of the initial and final stationary states of an electron transition, the transition probabilities yield selection rules, emission line intensities, and absorption cross sections. The former governs whether a transition is permitted or forbidden. The amplitudes of the latter two are often written as oscillator strengths. In this chapter, we describe the formalism for determining selection rules and oscillator strengths. We begin with the Schrödinger model and generalize to fine structure transitions for bound-bound transitions. We then address the oscillator strengths of bound-free transitions. Finally, we derive the line spread function describing the natural line width, which depends on the magnitude of the Einstein coefficients and is written in terms of the damping constant. Full expressions for the bound-bound and bound-free absorption cross sections are provided.

Chapter 16 begins by showing how quantum mechanics explains the structure and basic properties of multielectron atoms and their position in the periodic table of elements. It introduces the main approximation methods that have been developed to study such systems, explains the atomic shell structure, and discusses the helium atom in detail. It then looks at the different types of forces that bind atoms together to form molecules, focusing on diatomic molecules and the hydrogen molecule in particular. It discusses the long-range intermolecular forces that are responsible for many of the chemical and structural properties of matter, and identifies the zero-point or vacuum field as being responsible for the van der Waals and Casimir forces. In the final section, the properties of atomic nuclei are shown to reveal an internal structure with periodicities reminiscent of those of atoms and to disclose the effect of the nuclear spin–orbit interaction.

Chapter 18 is entirely devoted to the quantum theory of scattering, which is normally covered in more detail in a course on quantum field theory. We introduce the main concepts, including scattering amplitude, differential and total cross sections, and form factors, and derive the main formulas for elastic scattering, in a nonrelativistic framework; this allows us to appreciate how the information obtained from scattering experiments is used to explore the intricacies of quantum particles that are otherwise inaccessible. The Born approximation is studied and applied to scattering by a periodic potential, a weak potential, and Rutherford scattering. The partial wave expansion is derived and applied to obtain the optical theorem. The chapter concludes with a complementary section on resonant scattering.