Talk:PlanetPhysics/Klein Gordon Equation 3
Original TeX Content from PlanetPhysics Archive[edit source]
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: Klein-Gordon equation %%% Primary Category Code: 03.65.Db %%% Filename: KleinGordonEquation3.tex %%% Version: 13 %%% Owner: bci1 %%% Author(s): bloftin, bci1 %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}
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\begin{document}
This is a contributed Topic.
\section{The Klein-Gordon (KG) Scalar Relativistic Wave Equation}
{\bf Remarks:}
The KG-equation is a Lorentz invariant expression.
For specific \htmladdnormallink{computations}{http://planetphysics.us/encyclopedia/LQG2.html} of specific cases it can only be utilized with the appropriate \htmladdnormallink{boundary}{http://planetphysics.us/encyclopedia/GenericityInOpenSystems.html} conditions.
\subsection{1.1. The Klein-Gordon equation} The Klein-Gordon equation is an equation of \htmladdnormallink{mathematical physics}{http://planetphysics.us/encyclopedia/PhysicalMathematics2.html} that describes spinless (spin-0 \htmladdnormallink{particles}{http://planetphysics.us/encyclopedia/Particle.html}). It is given by: \[ \Box \psi = \left(\frac{mc}{\hbar }\right)^2 \psi \] Here the $\Box$ symbol refers to the \htmladdnormallink{wave operator}{http://planetphysics.us/encyclopedia/DAlembertOperator.html}, or D'Alembertian, ($\Box = \nabla^2 - \frac{1}{c^2} \partial^2_t$) and $\psi$ is the \htmladdnormallink{wave}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} \htmladdnormallink{function}{http://planetphysics.us/encyclopedia/Bijective.html} of a spinless particle.
\subsection{1.2. Relativistic energy levels of a spinless particle in a Coulomb field}
\subsection{1.3. Relativistic invanance of the de Broglie relations}
\subsection{1.4. Relativistic energy-momentum relation of a free particle}
\subsection{1.5. Charge and current density}
\subsubsection{1.5.1. Charge and current density in the presence of an electromagnetic field} \subsection{1.6. Nonrelativistic limit}
\subsection{1.7. The initial data problem}
\subsection{1.8. Indefiniteness of the sign of charge}
\subsection{1.9. Interaction with an external electromagnetic field}
\subsection{1.10. Fine structure constant}
The case $Za > l/2$
test
\end{document}