# Which particles obey Klein-Gordon equation and why?

## 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].

What is difference between Klein-Gordon and Dirac’s equation?

The Klein-Gordon field gives a spin 0 representation, while the Dirac equation gives two spin 1/2 representations (which merge to a single representation if one also accounts for discrete symmetries). The components of every free field satistfy the Klein-Gordon equation, irrespective of their spin.

Is the 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?

. From equation (1.34) we see that the Klein–Gordon action is Lorentz-invariant.

What is the Klein-Gordon field?

In quantum field theory the corresponding Klein-Gordon field is characterized by “particles” with rest mass m and no other structure (e.g., no spin, no electric charge, etc. .) So the Klein-Gordon field is physically (and mathematically, too) the simplest of the relativistic fields that one can study.

19} for more on how these numbers arise physically from symmetries of nature. It may be noted that Schrödinger wrote down the Klein-Gordon equation first. But when he added the Coulomb potential, he was not able to get the energy levels of the hydrogen atom.

## Is the Schrodinger equation Lorentz invariant?

The Schrodinger equation is not Lorentz Invariant, so it cannot be applied to the wave functions of moving particles. However, the Classical Wave Equation is Lorentz Invariant and is also satisfied by particle wave functions.

Why do we need relativistic wave equation?

In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light.

What are the drawbacks of Klein-Gordon equation?

Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot take place.

### Is Schrodinger’s equation wrong?

In actual atoms, interelectronic Coulomb energy changes “dependent” on other Coulomb terms (= electron-nucleus ) and atomic kinds. This is the reason why Schrodinger equation is wrong, and cannot solve multi-electron atoms.

Is Schrodinger equation Galilean invariant?

FWIW: The Schrödinger equation is not only invariant under Galilean transformations. It is invariant under a larger group: the so-called Schrödinger Group.

Is Klein Gordon’s equation Lorentz invariant?

## Which equation is used in relativistic wave function?

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928.

Why We Use Klein-Gordon equation?

Klein-Gordon equation is considered a suitable equation for spinless particles, such as pions, described by spinless scalar field [45]. The idea of treating Klein-Gordon equation in quantum mechanical context only without further field consideration was forgotten.

How does relativistic quantum mechanics differ from non-relativistic quantum mechanics?

While the non-relativistic quantum mechanics (non-RQM) refers to the mathematical formulation of quantum mechanics in the context of Galilean relativity and quantizes the equations of classical mechanics by replacing dynamical variables by operators, the relativistic quantum mechanics (RQM) is the development of …

### Why Schrödinger equation is not suitable for each system?

Schrodinger’s equation cannot be solved exactly for atoms with more than one electron because of the repulsion potential between electrons. You can find more about that in any quantum chemistry textbook.

What is the physical significance of Schrodinger wave equation?

Schrodinger equation gives us a detailed account of the form of the wave functions or probability waves that control the motion of some smaller particles. The equation also describes how these waves are influenced by external factors.

• September 14, 2022