Jump to content

Talk:PlanetPhysics/Klein Gordon Equation 3

Page contents not supported in other languages.
Add topic
From Wikiversity

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}

\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}

\usepackage{html}

% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts}

% used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic}

% there are many more packages, add them here as you need them

% define commands here

\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}