When quantum electrodynamics, the quantum field theory of electrons and photons, was being developed after World War II, one of the major challenges for theorists was calculating a value for the Lamb shift, the energy of a photon resulting from an electron transitioning from one hydrogen hyperfine energy level to another.
The effect was first detected by Willis Lamb and Robert Retherford in 1947, with the emitted photon having a frequency of 1,000 megahertz, corresponding to a photon wavelength of 30 cm and an energy of 4 millionths of an electronvolt—right on the lower edge of the microwave spectrum. It came when the one electron of the hydrogen atom transitioned from the 2P1/2 energy level to the 2S1/2 level. (The leftmost number is the principal quantum number, much like the discrete but increasing circular orbits of the Bohr atom.)
Conventional quantum mechanics didn’t have such transitions, and Dirac’s relativistic Schrödinger equation (naturally called the Dirac equation) did not have such a hyperfine transition either, because the shift is a consequence of interactions with the vacuum, and Dirac’s vacuum was a “sea” that did not interact with real particles.