Talk:PlanetPhysics/Klein Gordon Equation 3

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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

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