Hydrogen and Positronium Radial Densities

We construct the radial density, the probability of the electron and positron beads being separated by a certain distance. (For hydrogen, this is the distance from the electron to the nucleus.)

Note that the hydrogen peaks around 1, whereas positronium peaks around 2. This means that if you look for an electron, you are more likely to find it closer to the nucleus in hydrogen than to the positron in positronium. It also means that positronium is more spread out and flimsy than hydrogen, which is important in an electric field.