- #1
good_phy
- 45
- 0
Hi.
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.
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.