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

[Mason Smith]

Homework Statement

Homework Equations

where

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?

 

[PeroK]

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?

 

[haruspex]

Further to PeroK's comment, you are asked to maximise P(r), not ∫P(r).dr.

 

[Mason Smith]

To PeroK and haruspex...thank you for the help! It makes perfect sense now.