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Hint needed in integral

  1. Nov 18, 2016 #1
    • Member warned about posting without the homework template
    Hello I have tried gaussian integrals does gaussian integrals have this general form formula??? if not then weather i do integration by parts or what just needed a hint to solve it correctly
     

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  3. Nov 18, 2016 #2

    BvU

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    Hello Core, :welcome:

    The template is there for a reason, don't erase it but use it; it will be to your benefit.

    What is the question ? and what is the relationship between your first line and the second ?
     
  4. Nov 18, 2016 #3
    I want to say in the pic I have tried many things here should I show the steps I tried?? just want a hint that how to correctly start this nothing more weather I substitute or use gaussian integral formula for expomentional that is sqrt(pie/a) then do integration by parts??
     
  5. Nov 18, 2016 #4

    BvU

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    My point is it seems you are trying to normalize the wave function $$\Psi(x,t) = A\, e^{-x^2/a^2} e^{-i\omega t} \sin kx $$ on the first line.
    But the second line does not reflect that ( it says ##\ \sin (2kx) \ ## instead of ##\ \sin^2 (kx) \ ## ).

    So :
     
  6. Nov 18, 2016 #5
    yes yes it is sin^2(kx) we can use 1-cos2(x)/2 formula here
     
  7. Nov 18, 2016 #6
    but that nasty exponential how to handle that
     
  8. Nov 18, 2016 #7
    it is liboff problem 3.15 I have found <p> that is zero but I stuck at A???
     
  9. Nov 18, 2016 #8
    these steps I have tried now where is mistake??
     

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  10. Nov 18, 2016 #9
    Now see here in this formula list there no formula for x^2 thats why I am stuck at this step needed a hint
     

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  11. Nov 18, 2016 #10
    how to integrate E^x^2/a^2 sinkx
     
  12. Nov 18, 2016 #11

    Mark44

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    For the latter expression, if you mean ##\frac{1 - \cos^2(x)}2##, use parentheses around the terms in the numerator. What you wrote means ##1 - \frac{\cos(2x)}2##. In any case, ##\sin^2(kx) \ne \frac{1 - \cos(2x)}{2}##. You have to consider that k mulitplier.
     
  13. Nov 18, 2016 #12
    thanks I am new to this website
     
  14. Nov 18, 2016 #13

    BvU

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    Maybe you want to check out number 6 here ?

    Otherwise there is CRC handbook of chemistry and physics, or Abramowitz (7.4.6)
     
  15. Nov 18, 2016 #14
    so if I use number 6 then can I change limits to 0 to infinity multiplied by 2 then It can be applied ???
     
  16. Nov 18, 2016 #15
    one thing more can I change sin(kx) in to exponentionals and then try to solve will it work or not??
     
  17. Nov 18, 2016 #16

    BvU

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    IF the function is even (##\ f(x) = f(-x)\ ##) then yes.
    You can give it a try... :rolleyes:
     
  18. Nov 18, 2016 #17
    what do you suggest now changing sin to exponential using euler formula or use this
     
  19. Nov 18, 2016 #18
    but cos(kx) is even ?? so I can use this to solve this nasty integral
     
  20. Nov 18, 2016 #19
    ok I am solving it by both methods and will tell you what I got
     
  21. Nov 18, 2016 #20

    BvU

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    Yes you can
    That would be the idea. But it doesn't look clean and quick to me, such a complex exponential...

    After all, integrating ##\ e^{-x^2}\ ## alone already requires ingenious mathematical manipulating...
     
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