In Chapter 11, we saw that by Wigner’s theorem, symmetry transformations in quantum theory are represented by unitary or antiunitary operators. Then, we focused exclusively in the symmetry of space rotations. Since our focus was so narrow, we did not have to introduce the most appropriate language for the description of symmetries, namely group theory.

In Chapter 9, we presented the quantum rule of combination of subsystems through the tensor product. In this chapter, we will discuss a key elaboration of this rule that applies to composite systems with a specific symmetry, namely, invariance under exchange of identical particles.

Spin was introduced as part of the effort to understand the structure of atoms prior to the development of mature quantum theory. Variations of Bohr’s model described atoms in terms of three quantum numbers, roughly similar to $n,𝓁$, and $m$ that appear when solving the Schrödinger equation in central potentials. In this context, Pauli proposed that, in each atom, there exists at most one electron for each triplet of quantum numbers. This proposal is Pauli’s famous “exclusion principle,” which we will analyze in Chapter 15.

This chapter explores interpersonal attraction, the subjective appeal of another person, which is often accompanied by a positive emotional reaction and an affiliative motivation for greater closeness to that person. This chapter organizes the many specific traits that enhance attraction in terms of characteristics that offer domain-general rewards (e.g., pleasure, self-esteem, belonging) and characteristics that advance specific evolutionary goals (e.g., survival, reproduction). The chapter then reviews the characteristics that are most consistently desirable, including physical attractiveness, social status, warmth/kindness, intelligence, proximity, familiarity, similarity, and reciprocity by reviewing relevant research findings, as well as exceptions and boundary conditions. The chapter ends with a review of how sociocultural factors, including the immediate situation, women’s reproductive cycles, and the broader relationship trajectories provide context for understanding romantic attraction.

Often there are situations in which the solutions to the time-independent Schrödinger equation are known for a particular potential but not for a similar but different potential. Time-independent perturbation theory provides a means of finding approximate solutions using an expansion in the known eigenfunctions.

This chapter focuses on the frameworks, or theories, that relationship scientists use to guide their study of romantic relationships. The chapter first explains evolutionary theory, which assumes that modern relationships reflect ingrained sex-specific adaptations to challenges derived from differential parental investment and affecting reproductive success. Next, the chapter reviews attachment theory, which contends that humans have an evolved attachment behavioral system that activates under threat and keeps people close to caring others. Attachment theory also explains how child–caregiver relationships can bias this attachment system, creating individual differences that persist into adulthood. A next major theory, interdependence theory, suggests that people rationally attempt to maximize their outcomes, though transformation of motivation can lead them to prioritize relationship outcomes as well. Finally, social ecological models highlight the role of the environment – and particularly stressful environments – to influence interpersonal dynamics. This chapter reviews, critiques, compares, and integrates each of the major theories that support relationship science.

This chapter explains the interventions that are used to repair and strengthen relationships. It starts with a description of common evidence-based therapeutic interventions, including forms of behavioral couple therapy and emotionally focused couple therapy. Then it reviews the evidence supporting short-term and long-term benefits of therapeutic interventions to improve relationship functioning. The second half of this chapter reviews educational interventions that can strengthen relationships and keep them from becoming distressed, including PREP, a widely used and adapted couple relationship education program. The chapter concludes with a discussion of how therapeutic and educational interventions can be strengthened by increasing their accessibility and by adapting them for minority (e.g., same-sex) couples.

The history of the laser dates back to at least 1951 and an idea of Townes. He wanted to use ammonia molecules to amplify microwave radiation. Townes and two students completed a prototype device in late 1953 and gave it the name maser or microwave amplification by stimulated emission of radiation.

The first step towards quantum theory was a response to a problem that could not be addressed by the concepts and methods of classical physics: the radiation from black bodies.

One of the most important concepts of classical mechanics is that of a closed system. A closed system is loosely defined as a system whose components interact only with each other, and it is characterized by phase space volume conservation and energy conservation – see Section 1.2.