The Birthday of Niels Bohr (1885) – Complementarity and Mathematics

Bohr’s complementarity principle says that quantum objects can exhibit both wave and particle properties, but not simultaneously. The mathematics behind this is the Heisenberg uncertainty principle: Δx Δp ≥ ℏ/2. The wavefunction ψ(x) and its Fourier transform φ(p) are complementary representations. Bohr’s institute in Copenhagen was a centre for quantum mechanics. He also worked on the liquid‑drop model of the nucleus (using surface tension mathematics) and helped found CERN. His debates with Einstein over quantum mechanics are legendary.