- #1

- 58

- 0

The eigenfunctions of the hydrogenic Hamiltonian are

[tex]\varphi[/tex][tex]_{nlm}[/tex]=R[tex]_{nl}[/tex]Y[tex]^{m}_{l}[/tex]

If I need to find the probability of finding the electron in the nucleus (in r<R0), and I use the normalized R[tex]_{nl}[/tex], can I simply calculate the integral

integral[0 -->R0] (|R[tex]_{nl}[/tex]|^2r^2)dr

?

without calculating the whole triple integral? the constants that should be obtained from the angular part of the integral are already included in the normalized R[tex]_{nl}[/tex] function?

And another question - we analyze the hydrogen atom as a two body problem, so the total Hamiltonian eigenfunctions have the form [tex]\varphi[/tex]CM[tex]\varphi[/tex]rel.

Why do we always consider only the relative part, and not the general solution?