Finding maximum of a wavefunction?

[smileandbehappy]

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]

 

[TSny]

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.

 

[smileandbehappy]

Thanks - feel a little foolish now... Here is my updated workings incase it's useful for someone in the future:

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

 

[TSny]

That looks good.