Nuclear Fusion Physics and Technology/Plasma Waves

Definition: Wave

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

Definition: Wave function

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

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