In 1914, Niels Bohr

In 1914, Niels Bohr obtained the spectral frequencies of the hydrogen atom after making a number of simplifying assumptions. These assumptions, the cornerstones of the Bohr model, were not fully correct but did yield the correct energy answers. Bohr's results for the frequencies and underlying energy values were confirmed by the full quantum-mechanical analysis which uses the Schrödinger equation, as was shown in 1925–1926. The solution to the Schrödinger equation for hydrogen is analytical. From this, the hydrogen energy levels and thus the frequencies of the hydrogen spectral lines can be calculated. The solution of the Schrödinger equation goes much further than the Bohr model however, because it also yields the shape of the electron's wave function ("orbital") for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds.

The Schrödinger equation also applies to more complicated atoms and molecules. However, in most such cases the solution is not analytical and either computer calculations are necessary or simplifying assumptions must be made.



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