Understanding what the SchrÃ¶dinger equation tells us about the structure of the atom is no simple task.
There were many lines in the spectrum of hydrogen. The electron was not making neat little transitions from one energy level to another. It was not traveling in circular or even elliptical orbits (Bohr tried those too...). What it was doing was vastly more complicated--or was it? Remember, Bohr's theory did not really explain the total behavior of the electron. It gave no answer as to why the electron did not eventually spiral into the nucleus. Bohr said that the electron simply "existed" in certain stationary states and jumped between them and them only.
Then in 1923 Louis de Broglie suggested a revolutionary hypothesis based on the possibility that moving matter might have some wave-like character associated with it.