# Eigenfunction

#### Poirot

##### Banned
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
Re: eigenfunction

The operator is defined as follows.

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