Eigenfunctions of an operator

1. Sep 3, 2007

buraqenigma

How can i prove that $$u(x)=exp(-x^{2}/2)$$ is the eigenfunction of $$\hat{A} = \frac{d^{2}}{dx^{2}}-x^2$$

2. Sep 3, 2007

meopemuk

You should check that

$$\hat{A} u(x)= \lambda u(x)$$

where $\lambda$ is a constant.

Eugene.

3. Sep 3, 2007

buraqenigma

Thanks sir.

thank you i remember it .