Phy5645/HydrogenAtomProblem

From PhyWiki
Jump to navigation Jump to search

(a) To find we simply take the volume integral of Note that and thus the dependence in the integral vanishes.

Therefore,

(b)

(c) We simply integrate over the spherical shell given by varying and with The spherical harmonics, as we have defined them, are already normalized, so that the probability per unit radial coordinate is

(d) We may read the orbital and magnetic quantum numbers directly off of the spherical harmonic, they are and Therefore,

and

Back to Hydrogen Atom