The 1925 revolution of matrix mechanics and how to celebrate it in quantum mechanics classes

In 1925, Heisenberg, Born, and Jordan developed matrix mechanics as a strategy to solve quantum-mechanical problems. While finite-sized matrix formulations are commonly taught in quantum instruction, the logic and approach of the original matrix mechanics is a lost art. In preparation for the 100th anniversary of the discovery of quantum mechanics, we present a historical and logical discussion of how matrix mechanics was discovered, and how it was used to solve quantum-mechanical problems. We focus on the harmonic oscillator to describe how quantum mechanics advanced from the Bohr-Sommerfeld quantization condition to matrix mechanics. While keeping to the spirit of the original work, we express results using modern ideas and notation, so they are easier to follow. We end with a discussion of why knowing this history and approach is useful for quantum information science.