Identifying the dependence of various time-independent wavefunctions

I'm tasked with finding the variables that each of the following wavefunctions depends on: (1) a free particle in 2 space (2) a free particle in 3 space (3) a hydrogen atom (4) a lithium atom.

for situations (1) and (2) I get $\psi(x,y)$ and $\psi(x,y,z)$. However, regarding situations (3) and (4), I'm unsure how to proceed - advice?

• Hydrogen atom has one nucleus (in 3D space) and one electron (in 3D space). Lithium atom one nucleus and 3 electrons. Help yourself! Once done, try some coordinate transformations from laboratory frame to something more local. – ssavec Mar 10 '16 at 16:34
• @ssavec I would love to figure this out myself, but I don't know how to interpret one nucleus and one electron in terms of a wavefunction. – Tunk Mar 10 '16 at 16:39
• you do not need to write the wavefunction, just find the variables. So 3 coordinates for electron and 3 coordinates for nucleus. – ssavec Mar 10 '16 at 16:46
• @ssavec wait, but spin... ;) – Wildcat Mar 10 '16 at 16:49
• @ssavec So I would have $\psi(r_e,\theta_e,\phi_e)$ for the electron and $\psi(r_n,\theta_n,\phi_n)$ for the neutron? – Tunk Mar 10 '16 at 16:53