Is u(x)=exp(-x^{2}/2) an Eigenfunction of \hat{A}?

[buraqenigma]

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

 

[meopemuk]

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

You should check that

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

where $\lambda$ is a constant.

Eugene.

 

[buraqenigma]

Thanks sir.

thank you i remember it .