Principles of Quantum Mechanics and Laws of Optics from a Fourier Transform Formula

Proving that a function f( r ) is identical to a series of wave-like functions exp(i k r ) with coefficients of expansion equal to its Fourier transform (FT), if existed, we deduce mathematically the principles and hypothesis that a century ago celebrated physicists utilized to found quantum mechanics, firstly the duality particle-wave principle of Planck and Einstein, the de Broglie relation between momentum and wavelength, the Planck relation between energy and wave frequency, the exclusion principle of Pauli, the Heisenberg incertitude relation, the Bohr theory of absorption-emission of photons. From this property we deduce also the property k FT r which leads to Schrödinger equation, all the laws of wave optics concerning reflections, refractions, polarizations, diffractions by one or many identical 3D objects, noticeably the deflections of light by the Sun