The Dirac equation is the more generalized form of the Schrodinger equation and accounts for relativistic effects of particle motion (say an electron) by using a second order derivative for the energy operator. If you have an electron that is moving slowly relative to the speed of light, then you can get away with the Schrodinger equation, which is first order in time. This makes no sense to me, Why is it that you need to bump the energy operator up to a second order once you get moving at close to the speed of light? Conversely, why does the energy shift to a first order derivative when the electron slows down. I haven't been able to find an explanation for this.