A vectorial form of the Schr\"odinger equation
  We rewrite the time dependent Schr\"odinger equation by using only three dimensional vector algebra and by avoiding to introduce any complex numbers. We show that this equation leads to the same conclusions than the "complex version" concerning the hydrogen atom and the harmonic oscillator. We show also that this equation can be written as a Maxwell-Amp\`ere equation. 
Guy Barrand
physics.gen-ph quant-ph