The Dirac Equation
To obtain a Lorentz invariant Schro¨dinger equation, we considered the square root of the Klein-Gordon equation. This had the disadvantage that the Hamiltonian H =
√ p 2 + m2 contains an infinite number of powers of p 2/m2, the
parameter in which the square root should be expanded. It would have been better to treat space and time on a more equal footing in the Schro¨dinger equation. This is what Dirac took as his starting point. As the Schro¨dinger equation is linear in p0 = i∂/∂t, one is looking for a Hamiltonian that is linear in the momenta p j = i∂/∂x j (= −p j ).