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 the equation of Dirac?

The Dirac equation. where p0 = ih∂/c∂t (the energy operator), e is the charge on the electron, A0 is the scalar potential associated with the electromagnetic field, c is the speed of light, α1 are 4×4 matrices derived from the Pauli matrices, p1 = -ih∂/∂x is a momentum operator (p2 = -ih∂/∂y, p3 = -ih∂/∂z).

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.

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.

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.

Is Dirac equation correct?

It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine details of the hydrogen spectrum in a completely rigorous way.

What is Dirac famous for?

Dirac is most famous for his 1928 relativistic quantum theory of the electron and his prediction of the existence of antiparticles.

Who gave Klein-Gordon equation?

Schrödinger himself formulated it earlier in his notes together with the Schrödinger equation [51]. 2ψ(t, x) . Unlike Schrödinger equation, the free Klein-Gordon equation is invariant under Lorentz transformation, thus it is an eligible candidate for relativistic quantum mechanical equation.

Is spin a relativistic effect?

In quantum physics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle’s spin with its motion inside a potential.

Is the Schrodinger equation relativistic?

The Schrödinger equation is a non-relativistic approximation to the Klein-Gordon equation. The properties (momentum, energy.) described by solutions of Schrödinger equation should depend in the proper way of the Galilei reference frame. In reality they don’t.

Is Dirac equation Lorentz invariant?

etc. matrices are the same in all inertial frames. Now that we have found the correct transformation rules for an infinitesimal Lorentz transformation, we can easily find those for a finite transformation by building it up from a large number of successive infinitesimal transforms.