If \(\Psi=\exp [\mathrm{i}(\mathrm{kx}-\omega \mathrm{t})]\), the complex function \(\psi(x, t)\) moves round and round the unit circle in the complex plane as x and t change, as illustrated in Figure...If \(\Psi=\exp [\mathrm{i}(\mathrm{kx}-\omega \mathrm{t})]\), the complex function \(\psi(x, t)\) moves round and round the unit circle in the complex plane as x and t change, as illustrated in Figure \(\PageIndex{1}\):. This contrasts with the back and forth oscillation along the horizontal axis of the complex plane represented by \(\cos (\mathrm{kx}-\omega \mathrm{t})\).
