Ciro Santilli @cirosantilli 35

Basically the same as matrix mechanics it seems, just a bit more generalized.

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:

Bibliography:

One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the phase space coordinates of Hamiltonian mechanics, which appear in the matrix mechanics formulation of quantum mechanics, which offers insight into the theory, particularly when generalizing to relativistic quantum mechanics.

One way to think is: what is the definition of space space? It is a way to write the wave function ${\psi }_x(x)$ such that:And then, what is the definition of momentum space? It is of course a way to write the wave function ${\psi }_p(p)$ such that:

physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508#39508 gives the best idea intuitive idea: the Fourier transform writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.

Bibliography:

This Heisenberg's breakthrough paper on matrix mechanics which later led to the Schrödinger equation, see also: history of quantum mechanics.

Published on the Zeitschrift für Physik volume 33 page pages 879-893, link.springer.com/article/10.1007%2FBF01328377

Modern overview: www.mat.unimi.it/users/galgani/arch/heisenberg25amer_j_phys.pdf