I'm reading Basdevant/Dalibard on 'Stationary States of the Hydrogen Atom' in preparation for a final this week, and the "Probability distribution function" for finding an electron in a spherical shell of thickness dr in the ground state is given.(adsbygoogle = window.adsbygoogle || []).push({});

It's not derived, so I was wondering if anyone could explain how to find such a distribution function.

Momentum, for example. If I wanted to find the probabilty distribution function for momentum, how would I do that?

I think I've got the wavefunction for the ground state of Hydrogen:

(using the equation involving spherical harmonics, the radial equation, and n=1, l=0, m=0)

[tex]|100>=(1/a_{o})^{2/3}e^{-r/a_{o}}\sqrt{1/{4\pi}}[/tex]

Any insight would be very much appreciated!

EDIT:

Oh, to clarify, Basdevant lists this as the answer for the radial probability distribution function:

[tex]P(r)dr=|\psi_{1,0,0}(r)|^2(4\pi)r^2dr[/tex]

I just don't know how he got there!

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# Probability Distribution Function, H-atom

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