It thus combines quantum mechanics with the theory of relativity. Dirac's equation is a model for (a) electron and positron (massive case), (b) neutrino and antineutrino (massless case). The left side represents the square of the momentum operator divided by twice the mass,which is the non-relativistic kinetic energy. The second purpose is to treat the Dirac equation in relativistic quantum theory. The nuclear physicist Niels Bohr described Dirac as "the purest soul in physics". The puzzle that he wanted to solve was that if electrons have positive energy (which they really have) and when a photon interacts with this electron, an electron will decay into negative energy. Writers. 1 Derivation of the Dirac Equation 1 2 Basic Properties of the Dirac Equation 4 3 Covariance of the Dirac Equation 13 4 Construction of the Matrix S() 20 . The first one is to give an updated and self-contained explanation of the strategy to study the evolution of superoscillations by referring to the quantum-mechanical Schrdinger equation and its variations. Dirac's equation is a relativistic wave equation which explained that for all half-spin electrons and quarks are parity inversion (sign inversion of spatial coordinates) is symmetrical. Step Explanation Since the Lorentz transformation must be linear the general form should look like: We wish now to find B, D, G, and H. These coefficients . Dirac's explanation: The hole theory With no other option left, Dirac thought of an explanation to these particles with negative energy. . The Dirac equation has made it possible to obtain a more accurate formula of the energy levels of hydrogen and hydrogen-like atoms, which includes the fine structure of the levels; it has also helped explain the Zeeman effect. Okay, so the rst attempt at deriving a relativistic Schr odinger equation didn't quite work out. explain their absence.