Non-mathematical philosophy of quantum mechanics.

[scorpion990]

I've been studying undergraduate level quantum chemistry, and I have a quick question. (Feel free to make the answers as mathematical as you want)

In the helium atom, does an individual wavefunction describe the state of a single electron, or the system in general (given an arbitrary but allowed energy level)? If it describes the entire system, how can the probability interpretation of the wavefunction be used?

 

[jtbell]

Strictly speaking, the wave function for a two-electron system such as helium, is a single function of six position variables (three for each electron) plus time: $\Psi(x_1, y_1, z_1, x_2, y_2, z_2, t)$. It gives the joint probability density for finding electron #1 at $(x_1, y_1, z_1)$ and electron #2 at $(x_2, y_2, z_2)$, at time t.