deletions | additions       diff --git a/Klein-Gordon Equation.tex b/Klein-Gordon Equation.tex  index 60fff16..f99add6 100644  --- a/Klein-Gordon Equation.tex  +++ b/Klein-Gordon Equation.tex 
...
$$\hbar^2 (-\partial_{ct}^2 +\nabla^2) \psi = M^2 c^2 \psi$$  $$-\hbar^2\partial^\mu\partial_\mu \psi = M^2c^2 \psi$$  \begin{enumerate}     \item Problems \subsection{Problems  with K-G. K-G.}  Problem: $|\psi|^2$ is no longer prob. density. Not conserved. 
...
Classical limit: $\ddot{\phi} = (c^2\nabla^2 -\frac{(Mc^2)^2}{\hbar^2})\phi \Longrightarrow \ddot{\phi} = (c^2\nabla^2 - \omega_{min}^2)\phi$  \item K-G \subsection{K-G  arises in CM physics physics}  \begin{enumerate}  \item $M=0$ case: $\ddot{\phi} = c^2 \nabla^2 \phi$. Dispersion relation: (Note, $c$ is the wave speed, not speed of light.) 
...
\end{enumerate}  \item Quantizing \subsection{Quantizing  K-G equation: $\ddot{\phi} = (\nabla^2 - m^2)\phi$ m^2)\phi$}  \begin{enumerate}  \item Action:  $$S[\phi(\mathbf{x},t)] = \int$$  \end{enumerate}    \end{enumerate}