"To visualize the standing waves (or orbitals) of electrons bound to a positively charged nucleus in three dimensions, we will need a four-dimensional plot of the wave function vs. x, y, and z." http://www.grandinetti.org/electron-orbital-shapes "The wavefunctions in the N=2 family are vectors in an abstract four-dimensional space. This can also be called a function-space and/or a Hilbert space." http://www.av8n.com/physics/wavefunctions.htm So, what are those dimensions and wave functions? This must be fairly basic.