Kramer studied from 1912 in theoretical physics at the University of Leiden, especially with Paul Ehrenfest. In 1916 he received his doctorate in Leiden. In Copenhagen he worked as an employee of Niels Bohr on quantum theory. In 1924 he was a lecturer at the Institute for Theoretical Physics in Göttingen.
Together with Niels Bohr and John C. Slater, he published work, " The quantum theory of radiation ," in the strict validity of conservation of energy has been questioned for the first time.
In 1926 he became Professor of Theoretical Physics at Utrecht University, where he earned a special formalism for the theory of the multiplet structure of the spectra developed, among others ( 1930). In 1934 was made a professor at the University of Leiden, where he became the successor of Paul Ehrenfest.