{c}
{wiki=Klein–Gordon_equation}

A relativistic version of the <Schrödinger equation>.

Correctly describes <spin 0> particles.

The most memorable version of the equation can be written as shown at <klein-Gordon equation in Einstein notation>{full} with <Einstein notation> and <Planck units>:
$$
\partial_i \partial^i \psi - m^2 \psi = 0
$$

Has some issues which are solved by the <Dirac equation>:
* it has a second time derivative of the <wave function>. Therefore, to solve it we must specify not only the initial value of the wave equation, but also the derivative of the wave equation, 

  As mentioned at <Advanced quantum mechanics by Freeman Dyson (1951)> and further clarified at: https://physics.stackexchange.com/questions/340023/cant-the-negative-probabilities-of-klein-gordon-equation-be-avoided[], this would lead to negative probabilities.
* the modulus of the wave function is not constant and therefore not always one, and therefore cannot be interpreted as a probability density anymore
* since we are working with the square of the energy, we have both positive and negative value solutions. This is also a features of the <Dirac equation> however.

Bibliography:
* <video Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)> at https://youtu.be/OCuaBmAzqek?t=600
* <An Introduction to QED and QCD by Jeff Forshaw (1997)> 1.2 "Relativistic Wave Equations" and 1.4 "The Klein Gordon Equation" gives some key ideas
* <2011 PHYS 485 lecture videos by Roger Moore from the University of Alberta> at around 7:30
* https://www.youtube.com/watch?v=WqoIW85xwoU&list=PL54DF0652B30D99A4&index=65 "L2. The Klein-Gordon Equation" by doctorphys
* https://sites.ualberta.ca/~gingrich/courses/phys512/node21.html from <Advanced quantum mechanics II by Douglas Gingrich (2004)>
  * https://sites.ualberta.ca/~gingrich/courses/phys512/node23.html gives <Lorentz invariance>


Klein-Gordon equation

http://fafnir.phyast.pitt.edu/py3765/ Phys3765 Advanced Quantum Mechanics -- QFT-I Fall 2012 by E.S. Swanson mentions several milestone texts including:
* <Advanced quantum mechanics by Freeman Dyson (1951)>


Quantum electrodynamics bibliography

{c}

TODO understand in detail.

<Advanced quantum mechanics by Freeman Dyson (1951)> mentions:
> A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.

<Atom 2007 Mini Series episode 3>:
> \[The <Dirac equation>\] could only describe a single electron. It fails completely to explain what happens when there is more than one electron present. What was needed was a new theory. A theory which explains how electrons interact with each other. 


The Dirac equation does not work for more than one electron

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{tag=Work by Freeman Dyson}

https://arxiv.org/abs/quant-ph/0608140v1

Lecture notes that were apparently very popular at <Cornell University>. In this period he was actively synthesizing the revolutionary bullshit <Richard Feynman> and <Julian Schwinger> were writing and making it understandable to the more general <physicist> audience, so it might be a good reading.

> We shall not develop straightaway a correct theory including many particles. Instead we follow the historical development. We try to make a relativistic quantum theory of one particle, find out how far we can go and where we get into trouble.
Oh yes, see also: <Dirac equation vs quantum electrodynamics>.


Ciro Santilli @cirosantilli 37

 Incoming links: Advanced quantum mechanics by Freeman Dyson (1951)