Understanding Normalization Factors in Scientific Research

[M. next]

How is it that:

See figure:

Given: See figure too

In details, I don't get the maths and simplification that took place!
Thanks!

 

[dextercioby]

Well, what is [exp(-x^2)]^2 equal to ?

 

[M. next]

exp(-x^4)

 

[jtbell]

Remember, exp(a) = e^a. So exp(a)exp(a) = (e^a)(e^a) = ... ?

 

[M. next]

it is supposed to be e^2a.
Correct me if am wrong.

 

[jtbell]

Right. So that should tell you what [e^(-x^2)][e^(-x^2)] is.

 

[TheDragon]

woah get your math straight.
that's not true: exp(a^2) =(e^a)(e^a)
the integral of exp[-x^2] is defined only from -infinity to infinity.