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The Klein-Gordon equation is a relativistic wave equation derived from the relativistic Energy-Momentum equation. It was first introduced by Schrödinger, Gordon, and Klein in the 1920s. However, Paul Dirac rejected it as a candidate relativistic equation due to its non-linearity in time and lack of sufficient relativism. The equation has a probability density that can have both positive and negative values, making it unsuitable as a single-particle wave equation.

In momentum space, the traditional position operator is not Hermitian, and therefore not an observable. To address this issue, the Pryce-Wigner position operator is introduced by "splitting the difference" and sharing the term on both sides of the equation, making it Hermitian. This operator is a relativistic generalization of the traditional position operator and is suitable for use with the Klein-Gordon equation.

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The Klein-Gordon equation is a relativistic wave equation derived from the relativistic Energy-Momentum equation.

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