How to prove $$\lim_{\alpha\rightarrow\infty} \frac{\sin^2\alpha x}{\alpha x^2} ~=~\pi\delta(x)~?$$
I have encountered this limit while learning time dependent perturbation and transition probability in Sakurai. How to show this limit? I tried to integrate around $x=0$ but didn't get anything useful? I am out of ideas. Any help is appreciated.
No comments:
Post a Comment