Wavefunction(s) of an $N$ electron atom Consider an isolated atom consisting of $N$ electrons. Does each electron have a wavefunction of its own (as is generally spoken about in fields like spectroscopy) or does our isolated atom have a single collective wavefunction?
 A: The $N$ electrons need to be described by a single collective wave function
$$\Psi(\vec{x}_1,m_{s1},\dots,\vec{x}_N,m_{sN},t)$$
where $\vec{x}_i$ are the space coordinates of the electrons,
$m_{si}$ are the spin quantum numbers ($+\frac{1}{2}$ or $-\frac{1}{2}$), and $t$ is time.
Notice also, because electrons are indistinguishable fermions,
this wave function must be antisymmetric with respect to
interchange of any two electrons $i$ and $j$.
See also Wave function - Many particle states in 3d position space.
Nevertheless, in spectroscopy you often see
factorized wave functions like
$$\psi_1(\vec{x}_1,m_{s1})\ \psi_2(\vec{x}_2,m_{s2})$$
or (slightly more correctly) Slater-determinant-like wave functions like
$$\frac{1}{\sqrt{2}}\left(\psi_1(\vec{x}_1,m_{s1})\ \psi_2(\vec{x}_2,m_{s2})-\psi_2(\vec{x}_1,m_{s1})\ \psi_1(\vec{x}_2,m_{s2})\right)$$
But these wave functions are only approximative solutions
to the multi-electron Schrödinger's equation
which are valid only if the interaction between the electrons can be neglected.
