Equação de Klein-Gordon

$(◻+\frac{m^2{c}^2}{{\hslash }^2})\psi (x,t)=0$

onde

$(◻=\frac{{\partial }^2}{c^2\partial t^2}-{\mathrm{\nabla }}^2)$

então

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

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}