Matter Waves and Orbital Quantum Numbers
  The atom's orbital electron structure in terms of quantum numbers (principal, azimuthal, magnetic and spin) results in space for a maximum of: 2 electrons in the n=1 orbit, 8 electrons in the n=2 orbit, 18 electrons in the n=3 orbit, and so on. Those dispositions are correct, but that is not because of quantum numbers nor angular momentum nor a "Pauli exclusion principle".   Matter waves were discovered in the early 20th century from their wavelength, which was predicted by DeBroglie to be, Planck's constant divided by the particle's momentum. But, the failure to obtain a reasonable theory for the matter wave frequency resulted in loss of interest. That problem is resolved in "A Reconsideration of Matter Waves" in which a reinterpretation of Einstein's derivation of relativistic kinetic energy [which produced his famous E = mc^2] leads to a valid matter wave frequency and a new understanding of particle kinetics and the atom's stable orbits.   It is analytically shown that the orbital electron arrangement is enforced by the necessity of accommodating the space that each orbiting electron's matter wave occupies. 
Roger Ellman (The-Origin Foundation, Inc)