nLab amplitude

Idea

The amplitude of a wave is a measure for its maximal change with space and time.

Definition

For $n \in \mathbb{N}$ and $\mathbb{R}^n$ the corresponding Cartesian space, a plane wave is a function $\mathbb{R}^n \to \mathbb{C}$ of the form

$$\vec x \mapsto A e^{-2 \pi i \vec k \cdot \vec x} \,.$$

Here $a \in \mathbb{C}$ is the amplitude of the plane wave (while $\vec k$ s its wave vector).

Related concepts

• probability amplitude

• absolute value