Section 3.1 Introduction
We concluded the last chapter with de Broglie's hypothesis that all matter exhibits wave-particle duality, not just light. De Broglie's proposal is radical. Arguing that all matter has wave-like properties turns out to have far-reaching implications whose answers fundamentally change the way we view the laws of the universe. One important question is the following: waves are spread out over regions of space; so, where is the particle if it is acting like a wave?
In this chapter, we will discuss the interpretation of de Broglie's waves in terms of probability. An implication of this probabilistic description of matter waves is the well-known Heisenberg uncertainty principle, which states that a particle cannot simultaneously have a precise position and momentum. We will show that the uncertainty principle ends up solving one of the failures of classical physics: it explains why atoms are stable. The uncertainty principle also limits our ability to measure and manipulate matter at small, sub-atomic scales.
We finish the chapter with a generalization of de Broglie's relation — Schrödinger's equation — that can be used to calculate wavefunctions for particles.