This chapter and Chapter 5 together form an introduction to the Schrödinger equation in one dimension.

Following Chadwick’s discovery of the neutron in 1932, it might have seemed that all forms of matter could be explained as different combinations of fewer than 100 elements, and those elements in turn could be explained as different combinations of protons, neutrons, and electrons. Add photons to the list, and you pretty much had the universe summed up. This is the kind of model physicists like: complicated behavior arising from a few simple building blocks.

You probably learned in school that matter comes in three phases: solid, liquid, and gas. (A fourth phase called “plasma” only tends to occur in extreme environments like the center of the Sun or physics laboratories, so your teachers can be forgiven if they left it out.) Gases can flow and conform their shapes to their containers, and can also compress or expand; liquids can also flow and conform shape, but they cannot compress or expand; solids can’t really flow, conform, compress, or expand.

The story of atoms so far, in three parts: 1. 1911: Rutherford describes an atom as being made of small negatively charged electrons orbiting a large positively charged nucleus, all very analogous to planets orbiting the Sun. 2. 1913: Bohr addresses both of those problems by proposing that the angular momentum of an orbiting electron can only take on certain discrete values, and can jump discontinuously between those values. Like Planck’s resolution of the ultraviolet catastrophe and Einstein’s explanation of the photoelectric effect, this fits the data but does not provide any fundamental principles. 3. 1926: Schrödinger publishes his wave equation. Eventually, all the ad hoc hypotheses of the old quantum theory are seen to be consequences of Schrödinger’s wave mechanics.

Chapter 8 talked about atoms in isolation. But most of the atoms around you are joined together, a fact that can dramatically change their physical and chemical properties. In this chapter we explore atoms that are joined together in molecules. Chapter 11 will describe solids, large collections of atoms or molecules bound into a macroscopic size.

How would you model the air in your room?

In 1869 Dmitri Mendeleev presented to the Russian Chemical Society a periodic table and a set of laws that laid the foundation for modern chemistry. He showed that the elements could be placed in an order, corresponding loosely but not perfectly to their atomic weights, and this order could be used to classify and predict their properties. He was even able to predict the existence and properties of elements (such as gallium and germanium) that had not yet been discovered.

Einstein’s theories have become part of popular culture. The fact that time passes differently for different observers (“time dilation”) is a staple of science fiction, from Planet of the Apes (1968) to Interstellar (2014).