Source: cirosantilli/principal-quantum-number
= Principal quantum number
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Determines energy. This comes out directly from the resolution of the <Schrödinger equation solution for the hydrogen atom> where we have to set some arbitrary values of energy by <separation of variables> just like we have to set some arbitrary numbers when <solving partial differential equations with the Fourier series>. We then just happen to see that only certain integer values are possible to satisfy the equations.