Time-averaged position

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    Imagine you are standing in the middle of a large spherical room with a transparant, penetrable border. This room represents the nucleus of an atom. There is also a smaller spherical object that is orbitting your room. This object represents an electron. As part of an experiment you observe the motion of that ‘electron’ at different points in time and you measure the distance between your position and the position of the ‘electron’. Sometimes the ‘electron’ will be rather close to you, even inside your room, and other times the electron will be further away. After some time you stop your measurement and you look at your result. You will notice that some distances are more likely to occur than others. This distribution of distances describes the probability of finding the electron at a particular distance from the nucleus.

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