6.A: The helium wave function
A particle moving along one dimension, like the particle between two walls, is described by a wave function that depends on one spatial coordinate. A particle moving in three dimensions, like a single electron moving around a nucleus, is described by a wave function that depends on three spatial coordinates, x, y and z. The wave function gives the probability amplitude for finding the electron at the coordinates (x,y,z), and the square of the wave function gives the probability.
Now what happens when we get to a many-electron atom? Let's start with helium. There are two electrons, so stationary states for helium depend on x, y and z for each of the two electrons. The six-dimensional wave function for helium, shown here, is very difficult to plot, let alone calculate.