He reviewed Pauli Equation and Shrodinger Equation, which is not relativistic. Let’s derive Klein-Gorden Equation in relativistic framework, from E^2 = m^2 c^4 + p^2 c^2

hence the Klein-Gorden equation

Now we move on to see the genius of Dirac in deriving Dirac Equation by taking square root of an operator delta:

How does antimatter come out of Dirac Equation?

let’s study when the particle is at rest:

it’s a 4 by 4 matrix, hence there must be 4 solutions or eigen states:

The top two are normal negative electrons, the bottom two must be positive electrons.