Another route to quantum mechanics

Heisenberg’s matrices calculated spectra but offered little familiar imagery. Inspired by de Broglie’s matter waves, Erwin Schrodinger sought an equation resembling those for vibrating strings.

For a given potential, only certain energies allow wavefunctions that satisfy the boundary conditions. Bohr’s discrete levels now appeared as naturally as the allowed standing waves on a string.

Wavefunction and uncertainty Scientific model diagram electron described by ψ electron described by ψ Δx · Δp ≥ ℏ/2 Δx · Δp ≥ ℏ/2
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Diagram description

Static physics diagram: schrodinger_wavefunction.

What was waving?

Schrödinger hoped the electron was literally a spread-out material wave. Max Born proposed instead that ∣ψ∣2|\psi|^2 gives the probability density for finding it.

The theory no longer asked for the electron’s unseen orbit. It predicted the possible outcomes of measurements and their probabilities. Schrödinger disliked that interpretation and later invented his famous cat to expose the discomfort of carrying quantum superposition into everyday life.

Wave mechanics and matrix mechanics were soon shown to be equivalent. Two radically different ways of thinking had reached the same theory.