The motivation for the old quantum condition was the correspondence principle, complemented by the physical observation that the quantities which are quantized must be adiabatic invariants.
From this, (3) quantum mechanics can be seen to emerge via correspondence principle, as a nonrelativistic approximation for a theory of inertia in relativity.
Under the correspondence principle, a new scientific theory should reproduce the results of older, well-established, theories in those domains where the old theories work.
The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of large quantum numbers.
