Equação de Klein-Gordon

$\left(\Box +{\frac {m^{2}c^{2}}{\hbar ^{2}}}\right)\psi (x,t)=0$

onde

$\left(\Box ={\frac {\partial ^{2}}{c^{2}\partial t^{2}}}-\nabla ^{2}\right)$

então

${\frac {\partial ^{2}\psi }{\partial t^{2}}}=c^{2}\nabla ^{2}\psi -{\frac {m^{2}c^{4}}{\hbar ^{2}}}\psi$

no método das diferenças finitas:

\frac{\partial^2 \phi(x,t)}{\partial t^2} \approx \frac{\phi(x,t+\Delta t) - 2\phi(x,t) + \phi(x,t-\Delta t)}{(\Delta t)^2}