Before revision: Klein–Gordon equation The relativistic mass-energy relation: where again E = total energy, p = total 3-momentum of the particle, m = invariant mass, and c = speed of light, can similarly yield the Klein–Gordon equation: that is: Derivation The energy operator is easily derived from using the free particle wave function (plane wave solution to Schrödinger's equation, see here for derivation of this wave function).Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd Edition), R. Resnick, R. Eisberg, John Wiley & Sons, 1985, Starting in one dimension the wave function is The time derivative of Ψ is .
After revision: Klein–Gordon equation The relativistic mass-energy relation: where again E = total energy, p = total 3-momentum of the particle, m = invariant mass, and c = speed of light, can similarly yield the Klein–Gordon equation: that is: Derivation The energy operator is easily derived from using the free particle wave function (plane wave solution to Schrödinger's equation, see derivation of this wave function).Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd Edition), R. Resnick, R. Eisberg, John Wiley & Sons, 1985, Starting in one dimension the wave function is The time derivative of Ψ is .