Ideal Chain and Vector normalisation

[Mic :)]

Homework Statement

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.

Thank you very much!
Any help would be massively appreciated.

 

[vanhees71]

It's already said what is to be done: Integrate the probality distribution over all possible values of the random variables and then choose $A$ such that this integral gives 1.

 

[Mic :)]

It's already said what is to be done: Integrate the probality distribution over all possible values of the random variables and then choose $A$ such that this integral gives 1.

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.

 

[vanhees71]

Look for Gaussian integrals in your textbook!

 

[Mic :)]

Would the first step be to arrange it as A(e^-3R^2)(e0.5Na^2) ?

 

[vela]

No.