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In the case of the Schrodinger equation solution for the hydrogen atom, each orbital is one eigenvector of the solution.
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Remember from time-independent Schrodinger equation that the final solution is just the weighted sum of the eigenvector decomposition of the initial state, analogously to solving partial differential equations with the Fourier series.
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This is the table that you should have in mind to visualize them: https://en.wikipedia.org/w/index.php?title=Atomic_orbital&oldid=1022865014#Orbitals_table
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Ancestors

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