130_notes.dvi

The radial wavefunctions should benormalizedas below.

∫∞

0

r^2 R∗nℓRnℓdr= 1

• See Example 16.4.2:Compute the expected values ofE,L^2 ,Lz, andLyin the Hydrogen state
  1
  6 (4ψ^100 + 3ψ^211 −iψ^210 +

√

10 ψ 21 − 1 ).*

The pictures below depict the probability distributions in space for the Hydrogen wavefunctions.

The graphs below show the radial wave functions. Again, for a givennthe maximumℓstate has no
radial excitation, and hence no nodes in the radial wavefunction. Asellgets smaller for a fixedn,
we see more radial excitation.