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I tried to solve some problem that i should get probability density with which eigenstate of

momentum is chosen after momentum measurement by using [tex]<\varphi_{k}|\Psi>[/tex]

I faced some stuck integral problem such as [itex]\int_{k_o}^0\frac{sin^{2}(2x)}{2x^{2}}dx[/itex]

I transformed [itex]sin^{2}(2x) = \frac{1 - cos(2x)}{2}[/itex] so i obtained [itex]\int_{k_o}^0\frac{1-cos(2x)}{2x^{2}}dx[/itex] but i don't know next step because, [itex]\int_{k_o}^0\frac{1}{x^2}dx[/itex] go up to infinity,diverse.

i tried to do partial integral such as [itex]\int udv = uv - \int vdu[/itex] but encountered same problem.

How can i overcome this singular point problem? i convinced that [itex]\int_{k_o}^0\frac{sin^{2}(2x)}{2x^{2}}dx[/itex]

should be solved to convegence because graphic of [itex]\frac{sin^{2}(2x)}{2x^{2}}[/itex].

Please help me and give me an answer.

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# [Q] square of 'sinc function' integral

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