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Apparently

[itex]

\Psi(x) = Ax^ne^{-m \omega x^2 / 2 \hbar}

[/itex]

is an approximate solution to the harmonic oscillator in one dimension

[itex]

-\frac{\hbar ^2}{2m} \frac{d^2\psi}{dx^2} + \frac{1}{2}m \omega ^2 x^2 \psi = E \psi

[/itex]

for sufficiently large values of |x|. I thought this would be a simple matter of just plugging in the approximate solution into the harmonic oscillator equation and erase terms where large values of |x| reduces the term to 1 or 0.

However, this turned out to be harder than expected. The first thing I am wondering is whether my approach is correct.

Any help would be appreciated!

Regards,

Anders

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# Approx. Solution To Quantum Harmonic Oscillator for |x| large enough

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