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The application of Schrödinger's equation to the hydrogen atom leads to far more than an explanation of the atom's spectrum. Note that the orbital visualizations are of "real orbitals." See https://en.wikipedia.org/wiki/Atomic_orbital#Real_orbitals and https://en.wikipedia.org/wiki/Atomic_orbital#Orbitals_table A note on pronunciation: the Greek letter φ is pronounced by many in English as fye, but the Greek pronunciation is, I believe, fee. And, in any case, I use the fee pronounciation. Check out http://www.forvo.com/search/%CF%86/