Finding maximum of a wavefunction?

AI Thread Summary
The discussion focuses on finding the maximum of a wavefunction, with the user attempting to differentiate the squared wavefunction using the product rule. The user initially finds the maximum at r = 2a(naught) instead of the expected 4a(naught). They emphasize the importance of the volume element dV, which is proportional to r² in spherical coordinates. The conversation includes a request for feedback on their calculations, indicating a desire for clarity and correctness. Overall, the thread highlights common challenges in quantum mechanics related to wavefunction analysis.
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Homework Statement



http://[ATTACH=full]199743[/ATTACH] [ATTACH=full]199744[/ATTACH]

Question D.

[h2]Homework Equations[/h2]

[ATTACH=full]199745[/ATTACH]

[h2]The Attempt at a Solution[/h2]

The wavefunction is all real. So I can simply sqaure it... However when I do this and differentiate it using the product rule, I'm getting r = 2a(naught) as the maximum and not 4a(naught)... Any advice?

[ATTACH=full]199746[/ATTACH]
 

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The probability of finding the electron is some volume element dV is |ψ|2 dV. The dV is important.

In spherical coordinates, dV is proportional to r2.
 
Thanks - feel a little foolish now... Here is my updated workings incase it's useful for someone in the future:

2a4onjn.jpg


Please let me know if I've made any horrific mistakes.
 
That looks good.
 
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