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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Probability Distribution Function, H-atom

**Physics Forums | Science Articles, Homework Help, Discussion**