Nuclear Fusion Physics and Technology/Plasma Waves

Definition: Wave

Wave $\Psi _{n}$ is set of two functions $\Psi _{n}\equiv \{{\vec {A}}(t,{\vec {x}}):\mathbb {R} ^{4}\rightarrow \mathbb {R} ^{n},\varphi (t,{\vec {x}}):\mathbb {R} ^{4}\rightarrow \mathbb {R} \}$.

Definition: Wave function

Wave function $\Psi _{n}(t,{\vec {x}}):\mathbb {R} ^{4}\rightarrow \mathbb {R} ^{n}$ is function defined as

$\Psi _{n}(t,{\vec {x}})\equiv {\vec {A}}(t,{\vec {x}})e^{i\varphi (t,{\vec {x}})}$