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 .