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Mar
29
comment triple integral (quantum mechanics)
@joriki I understand your comment, I will try to be more interactive. I have to leave now, but I'll try to give it a fresh look later today and see if I can compute it to the end. I'll post what I come up with. Thanks!
Mar
29
comment triple integral (quantum mechanics)
Thanks to both! The new answer then: 2) $\int_o^\pi \sin^3\theta d\theta = 0$. Isn't it? If all those things are right, how does it end up giving $1 \over \sqrt 2 \pi$?
Mar
29
comment triple integral (quantum mechanics)
@joriki I did read your comment, but I couldn't follow the global process and decide if it was you or Willie Wong who was right, so I decided to answer Willie Wong's questions and that I could always come back later and do it again if something was indeed missing.
Mar
29
comment triple integral (quantum mechanics)
3) $\int_0^\infty \rho^4 e^{-\rho}d\rho = 4!(1/\rho)^5$ ? >> I don't really understand this last part. Basically I tried to apply the gamma function by trying to follow my text book's explanation.
Mar
29
comment triple integral (quantum mechanics)
2) $\int_0^\pi \sin^2\theta d\theta = \pi/2 -1/4$ ? || 3) $\int_0^\infty \rho^4 e^{-\rho}d\rho = 4!(1/\rho)^5 ?
Mar
29
comment triple integral (quantum mechanics)
I love it. Thank you so much for your step by step answer. I'm gonna try to go through it answering your test questions. 1. $\sin\phi\cos\phi =0$ because $\sin4\pi = 0$. Also $\int \cos^2\phi d\phi = x/2 + (1/4)\sin2x + \kappa $. Since $\sin4\pi = 0$ >> $\int \cos^2\phi d\phi = x/2 = \pi$
Mar
29
comment triple integral (quantum mechanics)
I see, thank you Didier. Where do you suggest I start?
Mar
29
comment triple integral (quantum mechanics)
I've corrected my attempt as best as I could based on your comments and I understand what you say, unfortunately I can't give up now. Thanks for your help; you did try.
Mar
29
comment triple integral (quantum mechanics)
added up until where I'm stuck
Mar
29
comment triple integral (quantum mechanics)
@joriki thanks for all those changes. I see now that I was missing many things I didn't know about. I'll be more crareful in the future. About the content I have most problems with the angular parts, but I didn't post anything, because I'm not so sure about the radial either. I'll try posting a bit of my reasoning to see if it is easier to point out where I'm wrong.
Mar
29
comment triple integral (quantum mechanics)
@joriki I don't see what else is wrong with the wave functions (I am copying them from a book). Could you be more explicit, please? maybe say exactly what the issue is?