Use of the Einstein-Brillouin-Keller action quantization

The Einstein-Brillouin-Keller semiclassical quantization and the topological Maslov index are used to deduce the correct quantum mechanical values for the energy of a one-electron atom (both nonrelativistically and relativistically) and a three-dimensional harmonic oscillator. The development is concise, transparent, and involves only elementary integral calculus and provides a conceptual and intuitive introduction to the quantum nature of the atomic and molecular structure of matter.