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Ideal Chain and Vector normalisation

  1. Sep 22, 2014 #1
    1. The problem statement, all variables and given/known data
    The questions are in the file.
    Hint:
    Part (a) asks you to find the normalization constant for P(N, R). Note that this is a 3D distribution: P(N, R)dRxdRydRz gives you the probability of finding R in a certain "differential volume" of size dRxdRydRz located at the vector position R. I would write P(N, R)=P(N, Rx)P(N, Ry)P(N, Rz) and normalize P(N, Rx), P(N, Ry) and P(N, Rz) independently. These have the same functional form (e.g. Gaussian), so you only have to find the normalization constant for one (say P(N, Rx)) and then cube the normalization constant to find the normalization constant for P(N, R). Note that Rx, Ry and Rz are vector components and run from -infinity to +infinity.


    I am particular unsure as to how to go about the first steps of A; ie finding the normalisation constant.

    Picture5.png

    Thank you very much!
    Any help would be massively appreciated.
     
    Last edited: Sep 22, 2014
  2. jcsd
  3. Sep 22, 2014 #2

    vanhees71

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    It's already said what is to be done: Integrate the probality distribution over all possible values of the random variables and then choose [itex]A[/itex] such that this integral gives 1.
     
  4. Sep 22, 2014 #3
    Hi! Could you please show me how?
    Thanks.
    I don't seem to be running on all cylinders right now, and need a bit a push.
     
  5. Sep 22, 2014 #4

    vanhees71

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    Look for Gaussian integrals in your textbook!
     
  6. Sep 22, 2014 #5
    Would the first step be to arrange it as A(e^-3R^2)(e0.5Na^2) ?
     
  7. Sep 23, 2014 #6

    vela

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    No.
     
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