Helium Wavefunction: Exploring 9 Coordinates & Time

[sidnake]

I'm doing about wavefunctions for my course, I'm a bit confused as to why the wavefunction of Helium has 9 coordinates and time and not 6 coordinates and time. As far as I was aware the wave function was used to describe the movement of electrons around the nucleus of an atom, and it was assumed the nucleus was stationary due to the high speed of the electrons. If the electrons can move in three dimensions, X,Y and Z then there should be three coordinates for one electron. Helium has two electrons so there should be 6 coordinates. Why is it that the wavefunction of Helium actually has 9 coordinates? Do you infact need to include coordinates of the nucleus? If anyone knows where I'm going wrong, please point it out to me.

 

[mfb]

As far as I was aware the wave function was used to describe the movement of electrons around the nucleus of an atom, and it was assumed the nucleus was stationary due to the high speed of the electrons.

For hydrogen, you don't need that assumption: You can separate the problem into a motion of the center of mass (and ignore this) and a relative motion between nucleus and electron - similar to the Kepler problem in classical physics. With 2 electrons, this is no longer possible. I would expect a good approximation with the assumption that the nucleus does not move (with an error of $\frac{m_e}{m_\alpha} \approx 0.01\%$), however.