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Eigenfunction

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Poirot

Banned
Feb 15, 2012
250
show that \(\displaystyle e^{-0.5x^2}\) is an eigenfunction of the operator \(\displaystyle \frac{d^2}{dx}-x^2\) and finds it's eigenvalue. I get \(\displaystyle e^{-0.5x^2}(x^2-1)-x^2\) so it doesn't seem like its an eigenfunction.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
Re: eigenfunction

The operator is defined as follows.

\[
\left(\frac{d^2}{dx^2}-x^2\right)f(x)=\frac{d^2f(x)}{dx^2}-x^2f(x).
\]