Finding maximum of a wavefunction?

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Homework Help Overview

The discussion revolves around finding the maximum of a wavefunction, specifically in the context of quantum mechanics. The original poster is attempting to analyze the wavefunction's properties and its implications for probability density.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to differentiate the squared wavefunction to find its maximum but encounters a discrepancy in the expected value. Some participants highlight the importance of the volume element in spherical coordinates, suggesting that the integration over the volume may affect the outcome.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's calculations. Some guidance has been offered regarding the volume element in spherical coordinates, indicating a productive direction in the exploration of the problem.

Contextual Notes

There is an indication of potential confusion regarding the application of the product rule and the role of the volume element in the context of the wavefunction's maximum. The original poster expresses concern about possible errors in their calculations.

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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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