Schrodinger Equation

When the Schrödinger equation is solved specifically for the hydrogen atom, the outcome is a set of possible electron energies (E) together with their corresponding wave functions ($\psi$), and — as a natural mathematical consequence of solving the equation — a set of THREE quantum numbers falls out automatically: the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (mₗ). This three-quantum-number solution successfully predicted the features of hydrogen's own emission spectrum, but it could not, by itself, explain the further splitting of spectral lines seen in the emission spectra of MULTI-electron atoms. That extra splitting was explained by George Uhlenbeck and Samuel Goudsmit in 1925, who proposed a fourth quantum number, the electron spin quantum number (mₛ). The wave function $\psi$ itself carries no direct physi …