The Dirac equation does not work for more than one electron Updated +Created
TODO understand in detail.
Advanced quantum mechanics by Freeman Dyson (1951) mentions:
A Relativistic Quantum Theory of a Finite Number of Particles is Impossible.
Atom 2007 Mini Series episode 3:
[The Dirac equation] could only describe a single electron. It fails completely to explain what happens when there is more than one electron present. What was needed was a new theory. A theory which explains how electrons interact with each other.