This chapter discusses the basic equations in quantum field theory.
First, we clarify some important properties of Maxwell equation so that the main part
of the electromagnetisms can be easily understood. Then, we present some useful
properties of the Dirac equation and its free wave solution. These two equations are
the basic ingredients in understanding quantum field theory. We also give the exact
energy spectrum of Dirac equation with Coulomb plus gravity potential in hydrogenlike
atom
Keywords: Maxwell equation, Dirac equation, photon, oscillator of electromagnetic
wave, free Dirac equation, energy eigenvalue in Coulomb and gravity.
