abstract-duncan-janssen

Anthony Duncan, University of Pittsburgh and Michel Janssen, University of Minnesota, U.S.A.
Stark contrasts between the old and the new quantum theory

We compare the treatments of the Stark effect in hydrogen in the old and the new quantum theory as given by Kramers in his 1919 dissertation and by Schrödinger in the third of his 1926 papers on wave mechanics, respectively. The two derivations are very similar, reflecting the close connection between the Schrödinger equation and the classical Hamilton-Jacobi equation central to the old quantum theory. Yet there are also important differences. In addition to the Bohr-Sommerfeld quantum conditions, the old quantum theory requires some artificial and physically not well motivated further restrictions on which orbits and which transitions between orbits are allowed. In wave mechanics, the quantum conditions emerge naturally and there is no need for any further special assumptions. We investigate which elements of the old quantum theory survived in the transition to the new quantum theory and which elements did not.