Hydrogen wave functions

The solutions to the Schrodinger equation for the hydrogen atom are given by (see, e.g., Schiff, "Quantum Mechanics", McGraw Hill 1980, p. 100)

Psi_{nlm}(r,th,ph) = N_{nl}R_{nl}(r)Y_{lm}(th,0).


In the following we plot radial functions R_{nl}, spherical harmonics Y_{lm}(th,0) and the corresponding total probability distribution P_{nlm}(x,y) for small values of n, l and m. More examples may be generated using the following, somewhat slow, Mathematica routines.

The colors in the plots of the probability distributions vary from blue to red corresponding to the increase of the probability from small (zero) to large values. To zoom in, click on the diagram.


n = 1 l = 0 m = 0
n = 2 l = 0 m = 0
l = 1 m = 0 & m = ±1
n = 3 l = 0 m = 0
l = 1 m = 0 & m = ±1
l = 2 m = 0 & m = ±1 & m = ±2
n = 6 l = 3 m = 0
n = 11 l = 6 m = ±3

pilch@physics.usc.edu