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Is there anyone who can help me with math?

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chicken
Posts: 6843 - Karma: 2,122
I'm trying to evaluate this integral

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the answer should be 1. I keep getting zero. Anyone able to get 1?


Jul 13 2012 1:56AM
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1337
Posts: 31038 - Karma: 29,003
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fixed
Jul 13 2012 1:57AM
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p.hawks
Posts: 2832 - Karma: 581
picture isn't working for me. Try reposting, or try wolframalpha, it can show you step by step. Cramster and hot math are also good, but only if its from a book, and you have to pay (or find someone who did)
Jul 13 2012 1:58AM
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ikindalikeskiing
Posts: 1381 - Karma: 142
Pic didn't show up for me but... Its summer and math is illegal
Jul 13 2012 1:58AM
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navierSTOKED
Posts: 858 - Karma: 33
pm me
Jul 13 2012 2:00AM
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fupaface
Posts: 810 - Karma: 449
I would just look up how to do it on youtube thats how i did all of my homework last year
Jul 13 2012 2:00AM
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chicken
Posts: 6843 - Karma: 2,122
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my attempt

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max karma if you figure it out!
Jul 13 2012 2:07AM
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ikindalikeskiing
Posts: 1381 - Karma: 142
I hope I never have to do that
Jul 13 2012 2:10AM
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LoathesRaisins
Posts: 3612 - Karma: 4,735
What kind of math is this OP?
Jul 13 2012 2:11AM
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iceberg.
Posts: 505 - Karma: 1,154
damn! why did africa do this to me>?
Jul 13 2012 2:36AM
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freeheelfool
Posts: 2 - Karma: 10
If you haven't figured it out yet, i don't think the conjugate should be equal.  In addition, you mixed up the change to b in the constant out front.  With those two the imaginary part drops and you end up with 1.
Jul 13 2012 2:44AM
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chicken
Posts: 6843 - Karma: 2,122
uh I don't really know. hence the frustration. It's for quantum physics but this is just a math/statistics problem. I have seen this kind of stuff in statistics but not with integrals like this. I just multiplied psi by its complex conjugate and am trying to integrate that over the interval (-infinity,infinity). However when I used integration for parts I get zero, and to be normalized it should be equal to one.

also for anyone trying to follow what I did. the integration in red from dv to v is correct I think. I just used an antiderivative I found on the wikipedia page for the error function.

However I just stumbled across the wikipedia page for gaussian integrals and the first paragraph mentions its applications in quantum field theory, which is a class that my prof teaches, so I might have a lead haha.

anyways it's gonna be an all nighter for sure. Last time I asked for homework help on NS you guys all killed it so I thought I'd try again
Jul 13 2012 2:57AM
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chicken
Posts: 6843 - Karma: 2,122
really? why is the conjigate not equal? the imaginary part dropping would be exactly what I want!

if I messed up the conjigate i'm going to be so mad!

+K
Jul 13 2012 2:59AM
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freeheelfool
Posts: 2 - Karma: 10
in the conjugate the imaginary part becomes negative
Jul 13 2012 3:21AM
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Mr.Gaga
Posts: 2021 - Karma: 542

^^ yeah he has it.

http://en.wikipedia.org/wiki/Complex_conjugate

In your Y*, the complex number change to negative, when you do Y*xY your Im part goes out.

Y*=(...)x(e^-ikx)x(...)
Y =(...)x(e^ikx)x(...)

YxY* = (...)^2x(..)^2 = [(b/Pi)^1/2] x [e^-bx^2]

Primitive of [e^-bx^2] is [(Pi/b)^1/2], so in the end you have 1

Jul 13 2012 4:22AM
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chicken
Posts: 6843 - Karma: 2,122
Thanks everyone. It was that I messed up the complex conjugate. I couldn't see why until I used euler's formula and then it is easy to see how the complex part cancels and the integration becomes much easier!

+K to all of you who helped out. We can let this die and get the math off the page before the kids wake up in the morning haha.
Jul 13 2012 5:19AM
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