Kronig left for that continent later in 1924 and paid visits to the important centers for theoretical-physics research in Germany and Copenhagen.

In January 1925, when Kronig was still a Columbia University PhD student, he first proposed electron spin after hearing Pauli in Tübingen.

Faced with such criticism, Kronig decided not to publish his theory and the idea of electron spin had to wait for others to take the credit.

Together with Isidor Isaac Rabi, Kronig gave the first solution (1927) of the Schrödinger equation for the rigid symmetric top.

In the beginning of May 1925, Heisenberg wrote three times to Ralph Kronig, with whom he had cooperated a little earlier in Copenhagen on the spectral theory of multi-electron atoms.

In the second letter, dated 5 May, Heisenberg wrote down in some detailed equations expressing the transition to his matrix mechanics.

In 1927, Kronig returned to Europe for good and worked in different prominent centres of research: Copenhagen, London, Zürich (where for a year he was Pauli's assistant).

He was recognized internationally by then as a renowned theorist who corresponded with the leading characters of that time and made interesting contributions to quantum mechanics and the application of it particularly on the physics of molecules and molecular spectra, an area on which he was the expert of those days.

Ralph Kronig (1931, 1932), published the first theory of x-ray absorption fine structure, which contained some of the basic concepts of the modern interpretation.

In the Kronig equation, energy positions Wn correspond to the zone boundaries, i. e. not the absorption maxima or minima, but the first rise in each fine structure maximum.

This model served as the starting point for all the subsequent short range order theories but few attempted to compare it to their data.

Hans Kramers and Kronig showed that this basic causality condition implies that the dispersion (i.e., the variation of refractive index with frequency) and the absorption are not independent.

It is not surprising that a relationship should exist, because dispersion and absorption are each related to the resonators described above in connection with scattering by bound electrons.