For any state in the hydrogen atom there are three important functions. These are shown above for the n=1, l=0 state. These are:

• in black, the radial wave function
• in red, the probability density function (this is essentially the square of the wave function)
• in blue, the radial probability distribution function (essentially the probability density function multiplied by 4πr²)

The radial probability distribution function shows how likely it is that the electron will be found a particular distance from the atom. For the n=1 state the most probable radius is, in fact, the Bohr radius.