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