If the electron is a wave, it cannot occupy “just any” orbit around the nucleus: it can only stay where its wave “finds itself again”, that is, where it does not interfere destructively with itself. From this idea the quantisation of the atom’s physical quantities — radii, energies, angular momentum — arises naturally, no longer varying continuously but only in discrete “steps”.

This section reconstructs Bohr’s model of the hydrogen atom: from the problem of classical instability, to de Broglie’s wave-based justification, to the four equations that give radii and energies, up to the direct experimental proofs (Franck-Hertz, photoelectric effect) and the consequences for electronic structure and spectra.

Try it — quantum simulator

In a potential well the energy is not continuous: only certain stationary wavefunctions are allowed, and their energies form discrete levels.

Quantum States (1D) simulator by Paul Falstad.