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Benedict Irwin added General Solution.tex
over 9 years ago
Commit id: c271ebe15b6504de7ddabfeda5fbe9ce53b66fd4
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\section{General Solution}
This has worked for time independent potentials. We wish to solve explicity for any time dependance, thus we let the wavefunction be of the form \begin{equation}
\psi=Re^{\frac{iS}{\hbar}}
\end{equation}
then the density is $\psi^*\psi=R^2$ and we may take the square root of this quantity for $R$. This leaves the general solution in 1D as \begin{equation}
\psi(x,t)=A\bigg[ \bigg]^\frac{-1}{2}e^{ikx}e^{-i\omega t}
\end{equation}
