(Biography at
http://www.pbs.org/wgbh/aso/databank/entries/bpschr.html
)
The Schrodenger equation examines the behavior of the electron strictly as a wave. I have never examined the intricate complexities of the exact solution, and I probably never will. I have examined the results of this "solution" and it does explain some of the behavior of atoms that the Bohr model is unable to explain.
Because of the Heisenberg uncertainty principle, one cannot determine the exact position of an electron. One can determine areas where there is a high probability of finding an electron. These areas of high probability are called orbitals. These orbitals are analogous to hotel rooms where people may be analogous to electrons. You may not know where a person is in the room but you know that they are in the room. The position of the electron in an atom is described by 4 quantum numbers. The first three quantum numbers describe the orbital.