Introduction

• Matter waves and wave functions
• Probability and the Born interpretation
• How particles can be in multiple places at once
• Heisenberg and quantum uncertainty

We will make a quantum jump of our own. Until now, we’ve been able to present a logical progression of quantum ideas that tracked, for the most part, with the historical development of quantum physics. By the early 1920s however, its development diverged into several different, though intimately linked, paths. We will visit each in turn, but for the sake of clarity we are going to hitch our wagon to the concept of quantum waves and wave mechanics. We will begin by introducing the star of this show, the quantum wave function.

Now that we’ve seen that particles of matter must possess wave properties, we will dive deeply into those waves. This will be important since matter waves are more difficult to understand than any kind of waves we are familiar with, even trickier than electromagnetic waves. We will see that the wavelike nature of matter has a lot of important consequences.

We will also learn how the everyday concept of probability penetrates to the very core of quantum physics. And, as anyone who has ever tried to plan a spring picnic around April showers can attest, probabilities are always accompanied by uncertainty. However, unlike uncertainty about the weather, we will see that uncertainty at the quantum level is so fundamental it can never be avoided. We will see that probabilities are required to describe both a particle’s location and its speed, and that in the quantum world we must abandon the comforting idea that particles follow definite paths as they move through space. This might seem like a step backward for science, but it has proven to be essential for understanding how nature really works at very small scales.