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The explanation of every observed detail of the hydrogen spectrum has gone hand in hand with the development of quantum mechanics. To quote Arthur Schawlow, co-inventor of the laser
"The spectrum of the hydrogen atom has proved to be the Rosetta stone of modern physics: once this pattern of lines had been deciphered much else could also be understood."

In this chapter we have followed part of this story, namely the development of the Bohr and Schrödinger quantum theories, and have indicated how the relativistic quantum mechanics of Dirac was needed to explain the observed fine structure of the hydrogen spectrum. To this day very high precision measurements of the hydrogen spectrum, using laser spectroscopic techniques, are still being use ( to test quantum field theory through the measurement of the Lamb shift which results from the interaction of the electron with its own quantized field.

When faced with the analysis of a complex situation, an approach commonly used in Physics is to make comparisons with simpler situations which have been analysed successfully and to use these solutions, and the underlying models, as starting points for the analysis of the complex situation. Complicating considerations are then introduced, in order of decreasing importance, as corrections to the simpler model.

The one-electron atom is a rare example of a real physical situation that can be analysed rigorously and analytically. It is no surprise, therefore, that its solution can be used as the starting point in the analysis of a wide range of situations in physics or that the models and notations used to describe the one-electron atom reappear frequently on other areas of physics. We have already seen how the one-electron atom solutions are carried into the description of multielectron atoms and in the final three chapters of Understanding Physics we will see how atomic solutions are carried into the analyses of molecules, of electron behavior in solids and of nuclei (the shell model).