  Matter waves were discovered in the early 20th century from their wavelength,
predicted by DeBroglie, Planck's constant divided by the particle's momentum,
that is, lmw = h/mv. But, the failure to obtain a reasonable theory for the
matter wave frequency resulted somewhat in loss of further interest.
  It was expected that the frequency of the matter wave should correspond to
the particle kinetic energy, that is, fmw = 1/2mv^2/h but the resulting
velocity of the matter of the particle, v = fmw x lmw, is that the matter wave
moves at one half the speed of the particle, obviously absurd as the particle
and its wave must move together.
  If relativistic mass is used (as it should in any case) the problem remains,
the same mass appearing in numerator and denominator and canceling. It is no
help to hypothesize that the total energy, not just the kinetic energy, yields
the matter wave. That attributes a matter wave to a particle at rest. It also
gives the resulting velocity as c^2/v, the wave racing ahead of its particle.
  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 of the atom's stable orbits.
