With the aid of private support he was able to study mathematics and physics at the University of Leiden, first having passed the exams required for students who had no gymnasium education.

Within a few months he co-authored a landmark publication with Bohr, on X-ray spectroscopy and the periodic system of the elements.

After Coster returned from Copenhagen he became Hendrik Lorentz' assistant at the Teylers Museum in Haarlem, where he developed an X-ray spectrometer.

[2] On 26 February 1919 he married Lina Maria "Miep" Wijsman, who held a degree in Oriental languages.

In 1938 he traveled to Berlin to convince Lise Meitner that she had to leave Germany to escape[1] the persecution of the Jews.

Together they went by train to Groningen; at the Dutch border, Coster persuaded German immigration officers that she had permission to travel to the Netherlands.

During the German occupation of Holland, Coster also helped Jews hide from the Nazis and listened to the BBC on a daily basis using a bicycle-powered radio.