Brief History of The Klein-Gordon Equation

In the early 20th century, Max Planck, Albert Einstein, De Broglie, Niels Bohr, Erwin Schroedinger, Heisenberg and others to produce a highly successful breakthrough in the world of physics. Where is that moment so many physical phenomena that can not be explained by the laws of physics that exist (Newton, Maxwell, etc.), such as Photoelectric effect, Black-body Radiation, the Zeeman effect, Stark effect, etc.. Great scientists are trying hard to explain these phenomena, until the breakthrough came on a new theory known as Quantum Mechanics.

Quantum mechanics is very successful in explaining these phenomena, so the theory can model the atom by matching the experimental results. In addition, with the help of Einstein's Special Relativity, quantum mechanics can also explain the phenomenon of nuclear physics, elementary particles, and other physical phenomena that the small size of the object relative to the displacement. Quantum mechanics with special relativity known as relativistic quantum mechanics. The first equation of the relativistic quantum mechanics was called as the Klein-Gordon equation.

Equation of relativistic quantum mechanics is called the Klein-Gordon equation derived from the name of two physicists, namely Oskar Klein and Walter Gordon, who in 1927 tried to explain the electron particles with special relativity approach. Unfortunately, because the electron has Spin ½, so the results are not satisfactory to explain the electron. Nevertheless, the Klein-Gordon equation can be explained very well to particle pieces (without Spin) and other particles that have integer Spins (0, 1, 2, ...). Pion are composite particles (yet to be discovered elementary particles that are not has Spin). For Spin particles, like electrons, can be explained very well by the Dirac equation.

Klein-Gordon equation was first considered by Schroedinger in search of equation for he wave-particle duality from de Broglie. Equations were found in his notes about the year 1925. He set up the equation to explain the hydrogen atom. Unfortunately, the Klein-Gordon equation fails to explain the fine structure of hydrogen atom spectrum. Energy levels are not produced in accordance with the Bohr's and Sommerfeld's atomic model which is the best at that time. In January 1926, Schroedinger replaces the Klein-Gordon equation by using non-relativistic equation, which is now known as the Schroedinger equation, to describe the hydrogen atom with a non-relativistic approach. The equation successfully describes the energy level in Bohr atomic hydrogen atoms without considering the fine structure. Schroedinger equation becomes phenomenal in the case of non-relativistic quantum mechanics.

The correct physical theory must satisfy the principle of relativity, ie, if a law of physics is true to a certain inertial system, then the equation must also be true for all other inertial systems. In addition, the particles in the quantum size is relatively small, which of course has a close to the speed of light. Therefore, the quantum equation must be in accordance with Einstein's theory of special relativity. To fit the theory of relativity, these equations must satisfy the Lorentz transformation. Unfortunately, the Schroedinger equation is only invariant with the Galilean transformation (Newtonian) and are not invariant to the Lorentz transformation (Relativity). Because it since the beginning of the Schroedinger equation using non-relativistic approach, so that Einstein's relativity theory has not been fulfilled in the equation. Thus, we must find a quantum equation that satisfy Einstein's theory of special relativity.

In 1926, soon after Schroedinger, Fock generalizations to the Schroedinger equation in an article for the case of a magnetic field that his style relies on speed and lowered independently of Klein-Gordon equation. Meanwhile, Klein and Gordon had to write a paper that obtained same equation. With the contribution of Fock, Klein-Gordon equation is often referred to as the equation of Klein-Fock-Gordon. Thanks to their efforts, relativistic quantum mechanics equations for free particles into an equation that has a simple plane wave solutions. The equations are quite successful in this regard is the Klein-Gordon equation for particles has integer Spin (0, 1, 2, ...). Furthermore the Dirac equation successfully describes for particle has half integer Spin (1/2, 3/2, 5/2, ...).