Benedict Irwin edited General Solution.tex  over 9 years ago

Commit id: 4b7fbc16eaf0b2153f36d7ba575f645d6ebf62a3

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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 $exp(-\pi x^2/2)$.