Hydrogen Atom

Abstract

Quantum mechanics of the atom of hydrogen, understood as a system consisting of a positively charged nucleus and a single negatively charged electron, is remarkable in many respects. This is one of the very few exactly solvable three-dimensional models with realistic interaction potential. As such it provides the foundation for much of our qualitative as well as quantitative understanding of optical properties of atoms at least as a first approximation for more complicated situations. A similar model also arises in the physics of semiconductors, where bound states of negative and positive charges form entities known as excitons, as well as in the situations involving a single conductance electron interacting with a charged impurity. Another curious property of this model is that the energy eigenvalues emerging from the exact solution of the Schrödinger equation coincide with energy levels predicted by the heuristic Bohr model based on a rather arbitrary combination of Newton’s laws with a simple quantization rule for the angular momentum. While it might seem as a pure coincidence of a limited significance given that by now we have harnessed the full power of quantum theory and do not really need Bohr’s quantization rules, one still might wonder by how much the development of quantum physics would have been delayed if it were not for this “coincidence.”