What does the Klein-Gordon equation describe?

What does the Klein-Gordon equation describe?

The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant. The wave function cannot therefore be interpreted as a probability amplitude.

What is the Klein-Gordon equation used for?

The Klein-Gordon equation [208,209] is a relativistic version of the Schrödinger equation that describes the behavior of spinless particles. The equation has a large range of applications in contemporary physics, including particle physics, astrophysics, cosmology, classical mechanics, etc.

What is problem with Klein-Gordon equation?

One can think that the main problem of the Klein-Gordon equation is that it is quadratic: if it wouldn’t be, we could expect negative energies to vanish and we could get a correct expression for a covariant quantum mechanic equation.

Which particles obey Klein-Gordon equation and why?

An equation obeying the laws of special relativity is the Klein-Gordon equation, KGE, which describes spin-0 particles with relativistic energy. Such a particle is the pi meson, the pion. A pion is a short lived subatomic particle that can take the place of an electron in an atom creating a pionic atom [1].

Is Klein-Gordon equation linear?

The Klein-Gordon equation is the linear partial differential equation which is the equation of motion of a free scalar field of possibly non-vanishing mass m on some (possibly curved) spacetime (Lorentzian manifold): it is the relativistic wave equation with inhomogeneity the mass m2.

What type of particles obey Klein-Gordon equation?

Is Klein-Gordon’s equation Lorentz invariant?

Therefore solutions of the Klein-Gordon equation are scalar or pseudoscalar, ie. invariant under spatial rotations and proper Lorentz transformations, and are invariant (scalar) or change sign (pseudoscalar) under space inversion.