Oct 27, 2013 Thread starter Banned #1 P 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.

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.

Oct 27, 2013 #2 E Evgeny.Makarov Well-known member MHB Math Scholar Jan 30, 2012 2,528 Re: eigenfunction The operator is defined as follows. \[ \left(\frac{d^2}{dx^2}-x^2\right)f(x)=\frac{d^2f(x)}{dx^2}-x^2f(x). \]

Re: eigenfunction The operator is defined as follows. \[ \left(\frac{d^2}{dx^2}-x^2\right)f(x)=\frac{d^2f(x)}{dx^2}-x^2f(x). \]