The Klein-Gordon Equation is a relativistic [wave equation,](The%20Wave%20Equation.md) that is, the [equation of motion](Equations%20of%20motion.md) for a charged [Spin-0 particle](Boson.md#Spin-0%20bosons) as well as a [classical scalar field](scalar%20field.md), $\varphi$. Where $\mu$ is some mass parameter, the Klein Gordon equation is expressed as $\frac{1}{c^2}\frac{\partial^2}{\partial t^2}\varphi-\nabla^2 \varphi + \mu \phi = 0$ where we usually compress it by replacing [Laplace operator](Laplace%20operator) and the time-derivative term with a [[d'Alembert operator]] such that we write it as $(\Box+m^2)\phi=0$ # Solutions # Derivations ## From Least Action Principle ## Quantum Mechanical Derivation # Non-linear scalar field equations A class of equations of a similar form to the Klein-Gordon equation are [[non-Linear Scalar Field Equations]]. #Mechanics/SpecialRelativity #QuantumMechanics/RelativisticQuantumMechanics #QuantumMechanics/QuantumFieldTheory #Mechanics/WaveMechanics #MathematicalFoundations/Analysis/DifferentialEquations/PartialDifferentialEquations