✎ Klein-Gordon Equation [The Physics Travel Guide]

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====== Klein-Gordon Equation ======

<note tip> $$( \partial _{\mu} \partial ^{\mu}+m^2)\Phi = 0 $$ 
-->Definitions#

* $\partial _{\mu} $ denotes the partial derivative and $\partial _{\mu} \partial ^{\mu}$ stands for a sum using the Einstein sum convention, i.e. $\partial _{\mu} \partial ^{\mu} =  \partial _0 \partial^0 - \partial _1 \partial^1 -\partial _2 \partial^2 -\partial _3 \partial^3$.
  * $m$ denotes the mass of the particle.
  * $\Phi$ is either the wave function of the spin $0$ particle if we use the Klein-Gordon equation in a particle theory, or describes the spin $0$ field if we work in a field theory.

<--

</note>
<tabbox Why is it interesting?>

The Klein-Gordon equation is the correct equation of motion that describes free [[basic_notions:spin|spin]] $1$ particles.

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student>

* A nice discussion can be found in [[http://www.quantumfieldtheory.info/website_Chap03.pdf |chapter 3 of Klauber's Student Friendly QFT book]]
  * For an elementary derivation of the Klein-Gordon equation see Physics from Symmetry by Schwichtenberg
 
<tabbox Researcher>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

--> Common Question 1#

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--> Common Question 2#

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<tabbox Examples>

--> Example1#

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--> Example2:#

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<tabbox History>

</tabbox>

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