A list of experiments and theories that progressively led physicists to quantum mechanics:
Early atomic models(~1897–1909):
First evidence that matter is composed of elementary constituents.
Thomson’s discovery of the electron and Rutherford’s nuclear model
established the existence of subatomic structure.
UV catastrophe & Planck’s quantization(~1900):
Crisis in classical electromagnetism caused by blackbody radiation.
Planck introduced quantization of energy per radiation mode,
introducing the constant that would later be known as Planck’s constant.
Bohr–Sommerfeld model(~1913–1916):
Semiclassical model for hydrogen-like atoms.
Quantization of angular momentum explained spectral lines.
Sommerfeld’s extension to elliptical orbits introduced early quantum numbers
and partially accounted for fine structure.
Photoelectric effect(1887–1905):
Observed experimentally by Hertz and theoretically explained by Einstein.
The light-quantization hypothesis accounted for the frequency threshold
and kinetic energy dependence.
Compton effect(~1923):
X-ray scattering experiment demonstrating momentum transfer
consistent with particle-like photons.
Wave–particle duality & de Broglie wavelength(~1924–1927):
Extension of quantization to matter.
Every particle is associated with a wavelength λ = h/p.
Confirmed experimentally by electron diffraction
(Davisson–Germer experiment) and later single-particle interference experiments.
Details on Planck quantization of the energy modes of Blackbody radiations.(~1900):
A semi-classical derivation inspired by statistical physics where Planck introduced his "bins" quantization idea.