Friday, November 16, 2018

mathematical physics - Transition probability derivation: How to prove $lim_{alpharightarrowinfty} frac{sin^2alpha x}{alpha x^2} ~=~pidelta(x)$?


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.




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classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

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