A Simple Way to Schrödinger's Equation

A century ago, in early 1926, Erwin Schrödinger published a series of papers culminating in a differential equation for a wavefunction $\psi$, describing wave-like properties of massive particles. This Schrödinger equation became the cornerstone of quantum mechanics since it allowed to solve numerous important problems in physics and chemistry. The whole development of quantum mechanics took decades, as it was based on the very limited experimental data, available at that time, and as it required a rethinking of the physical framework. However, it is surprising that even today, i.e. 100 years later, students may still have considerable problems in getting a good understanding of quantum mechanics. We attribute this to the fact that in common textbooks the chains of argumentation leading to the Schrödinger equation may have gaps or that the Schrödinger equation is introduced axiomatically. In order to give an easy access to quantum mechanics for bachelor students, this paper presents a direct bottom up path from particle diffraction experiments to Schrödinger’s equation. It relies solely on the experimental results, on fundamental physical laws and on undergraduate mathematics.