There are many mutually equivalent physical formulations of quantum mechanics. The two earliest and most well known are Schrodinger's wavefunction formulation and Heisenberg's matrix formulation. After that, there were attempts to generalize classical mechanics concepts into quantum mechanics, which saw the introduction of Bohm formulation and Wigner formulation, etc. However, it was until Richard P. Feynman, that a rigid connection between quantum mechanics and one of the most important quantity in classical mechanics, the action, was established.

In this worksheet, we started from the motivations of Feynman to introduce path integral quantum mechanics formulation, its physical interpretation and how it goes back to Schrodinger's picture, and an application on harmonic oscillators.

This worksheet uses the Maple Quantum Chemistry Toolbox.