We have been taught that the atomic orbitals we read about are probability density region of finding electrons of particular energies which are designated by the various quantum numbers.
Since, there is high degree of uncertainty when we talk about the position of merely the detection of an electron as well as the energy that we "observe" and which may pretty much not be the actual energy of the observed electron, what then is the significance of any atomic orbital?
I am not very well read in the various techniques and theories that we have developed over time, but still I think that atomic orbitals are at best a high probability region of finding certain electrons. Since we must not be able to do that with enough certainty how then can we check the validity of the existence of orbitals?
Is it possible, that the idea of atomic orbital is now outdated in terms of modern development and only used for simplistic explanations of complex electron motions and phenomenons?
Overall, I am interested in learning the significance of atomic orbitals. Google provides various links explaining the theory and listing its uses in modern chemistry but I could not find anything which properly explains the significance or even tries to explain the actual presence of something like an atomic orbital other than saying that we find so and so probability regions while working with Schrödinger equations.
Added after answers and comments: The answers are listing the uses of the contruct only, I tried to say that I am interested in finding out whether something like an orbital is actually there or not.
Maybe an example will help, there is no boundation for an electron of certain energy to move in an orbital that is dumbled or double dumbled shaped! I agree with electrons having certain energies described by quantum numbers, but how can one definitively prove that an electron belonging to say 2p_x resides in a dumbled shaped orbital?
Again, are orbitals true? Are they actually significant and not just a helpful mathematical construct? Can it be definitively proven?