Showing that the P(r) is maximum at r=a_0/Z

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Homework Help Overview

The discussion revolves around maximizing the function P(r) in a physics context, specifically relating to integration and the behavior of functions. The participants are exploring the mathematical reasoning behind finding the maximum value of P(r) at a specific point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the attempt to integrate a given equation over all values of r and question whether this approach is appropriate for finding the maximum of P(r). There is also a suggestion to reconsider the method of finding maxima in general.

Discussion Status

The discussion includes attempts to clarify the correct approach to maximizing P(r) rather than integrating it. Some participants express gratitude for the insights provided, indicating a productive exchange of ideas, though no consensus has been reached on a specific method.

Contextual Notes

There is mention of the integration leading to messy and divergent results, which raises questions about the assumptions and methods being used in the problem setup.

Mason Smith
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Homework Statement


upload_2019-1-27_11-10-43.png


Homework Equations


upload_2019-1-27_11-11-41.png

where
upload_2019-1-27_11-11-59.png


The Attempt at a Solution


I tried to integrate (7-32) over all values of r (i.e., from negative infinity to positive infinity) and set it equal to 1, but the result was too messy and was divergent. Am I making the right approach?
 

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Mason Smith said:

Homework Statement


View attachment 237887

Homework Equations


View attachment 237888
where
View attachment 237889

The Attempt at a Solution


I tried to integrate (7-32) over all values of r (i.e., from negative infinity to positive infinity) and set it equal to 1, but the result was too messy and was divergent. Am I making the right approach?
Why do you want to integrate? How do you normally find the maximum of a function?
 
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Further to PeroK's comment, you are asked to maximise P(r), not ∫P(r).dr.
 
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To PeroK and haruspex...thank you for the help! It makes perfect sense now. :smile:
 

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