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Benedict Irwin edited General Solution.tex
over 9 years ago
Commit id: 4b7fbc16eaf0b2153f36d7ba575f645d6ebf62a3
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index 86def0d..0de4ae3 100644
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Revision to the functional form. May want to revise form to be something like \begin{equation}
\psi=\frac{2}{c(0)}\big[ \psi=\frac{2}{\alpha}\big[ \frac{f(x)}{b(x)}+\frac{b(x)}{f(x)}
\big](c(0)-V(x))^k \big](\alpha-V(x))^k
\end{equation}
where
k $k$ is some constant
power and
c(0) $\alpha$ is the value of $f$ and $b$ when $f=b$.
This provided a brilliant match to the gaussian wavefunction of a harmonic oscillator potential, with normalised units. The constant $k$ was found to be around $13.35881$ for a spread of $x=[-3,3]$ and potential $V=x^2$, where the gaussian ground state was taken to be $exp(-\pi x^2/2)$.