Quantum mechanics is the physics of light and matter at the atomic scale. This chapter and the next will introduce the essentials of quantum mechanics in one dimension.

• Quantum mechanics will allow us to understand important properties of atoms and nuclei in Chapters 41 and 42.

• Despite the strange and unfamiliar aspects of quantum mechanics, its predictions are verified with amazing precision.

The probability of finding a particle at a particular position $x$ is determined by the particle’s wave function $\psi \left(x\right)$. This is a wave-like function that can be used to make probabilistic predictions, but nothing is actually waving.

• The wave function is an oscillatory function.

• The square of the wave function is the particle’s probability density.

• The particle is most likely to be found near the maxima of the probability density.

This chapter will focus on learning to interpret the wave function.

《 LOOKING BACK Sections 38.3–38.4 The photon model and the de Broglie wavelength

Quantum mechanics deals with probabilities. We cannot know exactly where an electron is or how it’s moving, but we can calculate the probability of locating the electron in a specified region of space.

• In an experiment with $N$ particles, if $N_{\text{A}}$ are detected in some region $\text{A}$ of space, then the probability of finding a particle in that region is $P_{\text{A}}=N_{\text{A}}/N$.

The wave function reconciles the experimental evidence that matter has both particle-like and wave-like properties. The probability of detecting a particle is governed by a wave-like function that can exhibit interference.

Because matter has wave-like properties, a particle does not have a precise position or speed. Our knowledge of the particle is inherently uncertain. This is reflected in the Heisenberg uncertainty principle, $\text{Δ}x\text{Δ}p\ge h/2$, where $\text{Δ}x$ and $\text{Δ}p$ are the position and momentum uncertainty.

《 LOOKING BACK Section 17.8 Beats