An equation related to this equation that uses the sine function instead of a constant multiplier is one of the few exactly solvable equations with soliton solutions.
One way of expressing this equation separates the positively and negatively charged free states so that they become basis elements and was formulated by Villars and Feshbach. In the time-independent case, this equation becomes the screened Poisson equation. Weisskopf and Pauli showed that this equation describes a spin-zero scalar field. An equation related to this equation that uses the sine function instead of a constant multiplier is one of the few exactly solvable equations with soliton solutions. Any component of any solution to the (*) Dirac equation is a solution to this linear equation. One major problem with using this equation originally was the fact that a naïve physical interpretation is indefinite probability density. This equation states that the mass squared times the wavefunction is equal to the negative d'Alembertian acting on a wavefunction. For 10 points, name this relativistic analogue of the Schrodinger equation.
One way of expressing this equation separates the positively and negatively charged free states so that they become basis elements and was formulated by Villars and Feshbach.
Klein-Fock-Gordon equation [require both underlined parts; prompt on "Sine-Gordon" at any point because I'm nice]