Never link two independent clauses with just a comma; this is known as a comma splice error. You can correct a comma splice in four ways:
In 1931 Oppenheimer attempted to find an equation for the photon that would
be an analogue to Dirac's equation for the electron, he failed
in this effort.
In 1931 Oppenheimer attempted to find an equation for the photon that would
be an analogue to Dirac's equation for the electron. He failed
in this effort.
In 1931 Oppenheimer attempted to find an equation for the photon that would
be an analogue to Dirac's equation for the electron; he failed
in this effort.
[or ". . . electron; however, he failed . . ."]
In 1931 Oppenheimer attempted to find an equation for the photon that would
be an analogue to Dirac's equation for the electron, but he
failed in this effort.
Although in 1931 Oppenheimer attempted to find an
equation for the photon that would be an analogue to Dirac's equation for the
electron, he failed in this effort.