Atomic Physics - normalising eigenstates

kel
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Homework Statement



Hi, I'd doing question 1 of the attached sheet and just wondered if someone could help me out. I'm a bit unsure of my calculus and need it reviewed, alsoam not entirely sure how to break down my workings (using the supplied equations in the hint) to find C. So any input would be greatly appreciated.


Homework Equations





The Attempt at a Solution



See the attached files - ps is there any software that I can use to write equations on this forum, mathtype would be nice, but I can't seem to cut & paste from it to here.

Thanks again
Kel
 

Attachments

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just realized that n=2 and alpha=2/a0, but still need some guidance on the calculus

cheers
 
Under "The attempt at a solution" you say "See the attached files" but there is no attempted solution in the files. One is just a statement of the problem and the other is just the integral set up but not computed- in spite of the fact that the problem statement tells you what that integral is!
 
the integral file is the one that I wrote out - wasn't sure if I've done the math correct before I move onto the next part.
 
Kel, since you mentioned you weren't able to paste a MathType equation into a forum post, I'm wondering if you or anyone else has had success pasting any sort of image into a post? I tried it and it didn't work out for me with JPG, PNG, or GIF images.

Bob
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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