Wave function

$\psi (x):{\mathbb{R}}^n\mapsto \mathbb{C}$ is the most common representation of a wave function, however any representation of elements in a Quantum Hilbert Space obeying the Schrodinger Equation for their time evolution, $i\hslash \frac{d}{dt}|{\psi }_t⟩=H|{\psi }_t⟩$, is considered to be a wave function.

In the above

• $H$, is the Hamiltonian,
• $\hslash$ is Planck’s reduced constant
• $|{\psi }_t⟩$ is a time evolving wave function.