Integral P(r) Normalization: Find Constant

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In summary, the conversation discusses the normalization of a function p(r) that is proportional to (1/r)Exp(-r/R), with the variable r and the constant R representing the proton radius. The speaker is struggling to find the integral of the function to equal 1 in order to determine the normalization constant and has tried using integration by parts but encountered discontinuities. They are seeking guidance on how to properly normalize the function.
  • #1
alfredbester
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p(r) is proportional too (1/r)Exp(-r/R). r is the variable.

I'm trying to normalise this function (R is proton radius), so I'm trying to get the integral between infinity and -infinity = 1 so I can find the normalisation constant. I don't know how to do this integral I've tried by parts but it seems there are discontuinities. I'm probably missing something obvious, can sombody point me on the right track?
 
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  • #2
:wink: Non-elementary solution.

http://mathworld.wolfram.com/ExponentialIntegral.html"
 
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  • #3
Thanks, I can't see how to normalise this function however.
 
  • #4
Probably you're integrating from [itex]r=0[/itex] to [itex]r=\infty[/itex], not over the whole range of r.
 

FAQ: Integral P(r) Normalization: Find Constant

What does "Integral P(r) Normalization" mean?

"Integral P(r) Normalization" refers to the process of finding a constant that will normalize a probability distribution function, P(r), so that the integral (or area under the curve) of the function is equal to 1. This is important for accurately representing the probability of events occurring within a certain range.

Why is finding the constant important?

Without finding the constant, the probability distribution function may not accurately represent the probability of events occurring. Normalizing the function ensures that the total probability is equal to 1, making it easier to interpret and use in calculations.

How is the constant calculated?

The constant is calculated by taking the reciprocal of the integral of the probability distribution function. This integral can be calculated using various mathematical methods, such as numerical integration or analytical techniques.

Can the constant change for different probability distributions?

Yes, the constant can vary for different probability distributions. It depends on the shape and range of the distribution. For example, a normal distribution will have a different constant than a uniform distribution.

What are the practical applications of "Integral P(r) Normalization"?

"Integral P(r) Normalization" is commonly used in statistics, physics, and other scientific fields to accurately represent and analyze data. It is also used in machine learning and data analysis to normalize input data for better performance and accuracy of models and algorithms.

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