The discovery of the photon was one of the major initiators of quantum mechanics.

Light was very well known to be a wave through diffraction experiments. So how could it also be a particle???

This was a key development for people to eventually notice that the electron is also a wave.

This process "started" in 1900 with Planck's law which was based on discrete energy packets being exchanged as exposed at On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).

This ideas was reinforced by Einstein's explanation of the photoelectric effect in 1905 in terms of photon.

In the next big development was the Bohr model in 1913, which supposed non-classical physics new quantization rules for the electron which explained the hydrogen emission spectrum. The quantization rule used made use of the Planck constant, and so served an initial link between the emerging quantized nature of light, and that of the electron.

The final phase started in 1923, when Louis de Broglie proposed that in analogy to photons, electrons might also be waves, a statement made more precise through the de Broglie relations.

This event opened the floodgates, and soon matrix mechanics was published in quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), as the first coherent formulation of quantum mechanics.

It was followed by the Schrödinger equation in 1926, which proposed an equivalent partial differential equation formulation to matrix mechanics, a mathematical formulation that was more familiar to physicists than the matrix ideas of Heisenberg.

Inward Bound by Abraham Pais (1988) summarizes his views of the main developments of the subjectit:

- Planck's on the discovery of the quantum theory (1900);
- Einstein's on the light-quantum (1905);
- Bohr's on the hydrogen atom (1913);
- Bose's on what came to be called quantum statistics (1924);
- Heisenberg's on what came to be known as matrix mechanics (1925);
- and Schroedinger's on wave mechanics (1926).

Bibliography:

- physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics on Physics Stack Exchange
- www.youtube.com/watch?v=5hVmeOCJjOU A Brief History of Quantum Mechanics by Sean Carroll (2020) Given at the Royal Institution.