Normalization and singularities

[Diego Floor]

Hi There!

Being direct to the point: Does normalization removes singularities? Such as infinite.

I came up with this question because, while I was working with a not normalized function, I reached a very strange result. There are two points where the probability tends to infininte.

Maybe that's because the function is not normalized. (intuitively, I thought the normalization would only re-scale the 'curve', when plotted) Or did I mess up the calculation?

If anyone wants to see more than that first question, I can show the equations I'm working. So we can have a more specific discussion. :)

[Avodyne]

Hi There! Being direct to the point: Does normalization removes singularities?
No.
I came up with this question because, while I was working with a not normalized function, I reached a very strange result. There are two points where the probability tends to infininte.
That's possible if the probability distriubtion is integrable at these points. For example, consider a classical harmonic oscillator with x=a\cos(\omega t). If you look at it at a random time, the probability that you will find it between x and x+dx is P(x)dx, with

P(x)={1\over\pi}\,{1\over\sqrt{a^2-x^2}

for -a\le x\le a, and P(x)=0 otherwise. P(x) becomes infinite at x=\pm a, but still \int_{-a}^{+a}P(x)dx = 1.

[Diego Floor]

Thanks! :D

I didn't remember that example, it really clarifies things out.

Ok, singularities are not evil! They just have a 'not so trivial' interpretation.