I am not sure about this. Hydrogen solution is derived using a time-independent potential, so the solution is constant in time(?)
Do you like playing in a carousel? Imagine playing it in a festival where some of the attractive stands are on the one side of the carouse, whereas on the other side it’s only empty space. When you are spinning inside, you will see from your point of view that in a certain time, your parents and other guardian make a crowd on the empty space to watch their kid playing the carousel. Whereas in the other side, people tend to make lines before going to the various attractive stands that are scattered. The number of people you see is the same as electron distribution in the 1s orbit, you can see that the number of people bulking on a certain position, spread evenly on the other, and nothing on certain areas.