Schrödinger's Equation
When Louis de Broglie published his hypothesis on matter waves—explaining that electrons exist as standing waves around an atom—it radically altered our understanding of matter.
However, like all models, de Broglie's had its limitations: it could only successfully describe single-electron systems like the hydrogen atom.
What physics needed was a generalized framework capable of describing electron behavior across multi-electron atoms. Enter Austrian physicist Erwin Schrödinger.
In 1926, Schrödinger mathematically derived a wave equation that accurately models the spatial distribution, energy levels, and wave functions (Ψ) of electrons bound within any atomic structure.
Schrödinger’s Equation is fundamental to understanding quantum mechanics and the behavior of electrons within the atom.
While the full mathematical derivation is complex, its physical implications are profound: instead of fixed circular orbits, electrons exist in 3D probability clouds known as atomic orbitals.
Watch the video to explore what Schrödinger’s Equation represents, how it replaces the Bohr model, and what it reveals about the fundamental nature of the electron.
Interactive that summarise everything that we have covered so far
This interactive (from pHET) allows you to compare the different models of the Hydrogen atom, (and thus test your understanding) starting from JJ Thomson's plum pudding model to Schrödinger