Conservation of Energy and Momentum of Drifting Electrons in Materials

In this research article, conservation of energy and momentum of drifting electrons in materials is expressed in a differential equation form. The equation is derived starting with Einstein’s mass-energy equivalence relation of 1905 for relativistic masses. The equation is valid for both small and large objects. Conservation of momentum is added to the equation and it is shown that Noether’s theorem is asserted. The drift velocity in metals is drastically reduced due to the much higher electron effective mass in metals.