  The explanation of the first-order Stark effect in hydrogen by Epstein and
Schwarzschild in 1916 was seen as a great success for the old quantum theory.
Yet, it also revealed some serious limitations of the theory. To recover the
experimentally found line splittings, one had to make some arbitrary
assumptions in addition to the basic quantum conditions to rule out certain
orbits. The calculation of intensities of lines on the basis of Bohr's
correspondence principle likewise required arbitrary additional assumptions.
Finally, the actual orbits predicted by the old quantum theory depend on the
coordinates chosen to impose the quantum conditions. Both Sommerfeld and
Epstein recognized this problem but offered no solution for it. All these
problems were solved in 1926 when Schr\"odinger and Epstein explained the Stark
effect on the basis of the new wave mechanics. The calculations in the two
theories are similar. In particular, both the Schr\"odinger equation in the new
theory and the Hamilton-Jacobi equation in the old theory are separated in
parabolic coordinates. The new quantum mechanics determines all allowed states
and transitions without any additional assumptions. It also replaced the
ambiguous guidelines based on the correspondence principle for calculating
intensities by the straightforward prescription that intensities are given by
the squares of the matrix elements of position, leading to results that agreed
much better with the experimental data. Finally, the embarrassing
non-uniqueness of orbits in the old quantum theory turned into the innocuous
non-uniqueness of bases of eigenfunctions in wave mechanics. To this day, the
Stark effect is remembered as one of the few qualified successes of the old
quantum theory. We suspect that this is largely because after 1926 it became
just one of the many unqualified successes of the new quantum theory.
