Kramers entered the University of Leiden in 1912 to study mathematics and physics. He graduated with his first degree on 27 October 1914. By this time, of course, World War I had begun and was affecting most of Europe. The Netherlands remained neutral during the war but it still had severe consequences for a young scientist like Kramers. He remained at Leiden after completing his first degree, and in 1916, while still undertaking research in theoretical physics under Paul Ehrenfest, he was appointed as a teacher at Arnhem Grammar School in Arnhem. On 7 June 1916 he was awarded the equivalent of a master's degree from Leiden.
At this point Kramers decided that he needed international experience but this was not easy given the fighting which engulfed much of Europe. On a scientific level he would have chosen to study with Max Born in Göttingen but because of the war this was out of the question. Denmark was, like the Netherlands, neutral so Kramers decided to travel to Copenhagen and study with Niels Bohr. This, however, was not without its problems since overland travel would have required him to go through Germany. Even travel by boat was not ideal since it had to go through waters which were, because of the war, declared unsafe. Nevertheless, travel by boat was the least bad option so Kramers took this route. He arrived unannounced and introduced himself to Bohr.
Now Niels Bohr had only been confirmed as being appointed to a chair of theoretical physics in Copenhagen in April 1916 while he had been working with Rutherford in Manchester, England, and had returned to Copenhagen in the summer of that year, not long before Kramers arrived. Bohr agreed to have Kramers as a student and under his supervision he wrote his doctoral thesis Intensities of spectral lines: On the application of the quantum theory to the problem of the relative intensities of the components of the fine structure and of the Stark effect of the lines of the hydrogen spectrum which he submitted to the University of Leiden. He was awarded his doctorate on 8 May 1919 and, in the same year, he was appointed as assistant to Niels Bohr, becoming Bohr's first assistant. His thesis, although submitted to Leiden, was published in the Memoirs of the Royal Danish Academy of Sciences and Letters. In his dissertation he carried out detailed calculations for the case of a hydrogen atom in an external electric field. This led him to a satisfactory interpretation of the intensities of Stark components (discovered by Johannes Stark in 1913). Kramers also included the effect of fine structure involving corrections for relativistic kinetic energy and coupling between electron spin and orbit.
In 1920 the Institute of Theoretical Physics opened in Copenhagen and Kramers, as Bohr's assistant, played a significant role in its establishment. On 25 October 1920 Kramers married Anna Petersen; they had three daughters and one son. In March 1924 Werner Heisenberg visited Kramers and Bohr at the Institute for Theoretical Physics in Copenhagen. Einstein was also visiting at this time. The interaction between Kramers and Heisenberg is particularly important as Radder relates in :-
The most significant achievement of Kramers in [this] period ... is his theory of optical dispersion, which is quite generally recognized as an important precursor of Heisenberg's matrix mechanics. At the heart of Kramers' theory are the correspondence principle and the so-called 'virtual field model' of the atom.Kramers returned to the Netherlands in 1926 when he accepted the position of professor of theoretical physics at the University of Utrecht. His inaugural lecture was Vorm en wezen. In addition to this post at Utrecht, he was also appointed professor at the Delft University of Technology in 1931. In 1933 he published Die Grundlagen der Quantentheorie which became a classic text. It was translated into English by Dirk ter Haar, a former student of Kramers, and published as Quantum mechanics in 1957. L Van Hove writes in a review:-
Kramers divided the subject into two parts, one dealing with the foundations of quantum theory and one presenting the quantum theory of the electron and of radiation. The whole volume, however, has great unity and it constitutes one of the very best presentations of quantum theory (nuclear phenomena excluded) every published. One of the attractive features is that the author went at all stages into an explicit discussion of the problems of interpretation and of relation to classical theory which are so delicate but form an essential part of the subject, and of which he had an excellent knowledge. Another fascinating aspect, which is now not only of scientific but also of historical importance, is the discussion of the interaction between electrons and the radiation field, which Kramers had brought at the time of publication of his book to its most advanced pre-war state of development by recognizing the necessity of what is now called mass renormalization. The fact that this masterly book was published as a volume of the Handbook of Chemical Physics, and perhaps also in later years the fact that the book was written in German, account for the lack of familiarity of many physicists of the younger generation with its contents.In 1933 Paul Ehrenfest, who was professor of theoretical physics at the University of Leiden, committed suicide. In the following year Kramers was appointed to succeed Ehrenfest, and he gave his inaugural lecture on Physics and physicists on 28 September 1934. He resigned from his appointment in Utrecht but continued to hold the chair at the Delft University of Technology. World War II began in 1939 and the German forces quickly overwhelmed the Dutch armies in the spring of 1940. Attempts were made to continue to run the country despite the German occupation but the University of Leiden was closed by the German occupational authorities in 1941, because students protested against the dismissal of their Jewish professors. It became clear that the closure was not going to be a short one and Kramers, like the other professors, had to find an income from other sources. He became a consultant for the Bataafsche Petroleum Maatschappij, one of the biggest companies in the Netherlands formed many years earlier from a merger of the Shell Transport and the Royal Dutch Petroleum Company. Kramers went to the company's offices in Amsterdam once a week. In October 1941 the Germans decreed that no Jews could be members of non-profit organisations. Kramers then resigned from the Royal Dutch Academy of Sciences in protest against the exclusion of Jews from the Academy.
In March 1943 Abraham Pais, who was Jewish, had gone into hiding in Amsterdam. Pais, who was also a physicist, knew Kramers well and had visited him regularly in Leiden from the autumn of 1939. Kramers learnt about Pais' hiding place in Amsterdam and visited him every Monday evening after he had completed his consultation work at the Bataafsche Petroleum Maatschappij. Pais writes that on these visits :-
Kramers and I would of course talk physics. In particular we had intense debates on questions having to do with the theory of the electron. Other subjects came up as well. Naturally we argued about the war situation. One day the discussion turned to music. Kramers said that my hiding period would be a good time for me to learn to play an instrument, and he offered to give me instruction on the cello, his personal favourite. I said that sounded great, except that I had no cello. That was not a problem, he replied, he knew a music store in Amsterdam where one could be rented.One day, in November 1943, the Gestapo came to the house where Pais was hiding. Kramers was there at the time. Pais went quickly to his hiding place and, by good fortune, was not discovered by the Gestapo. After they had left, Pais remained in his hiding place :-
... I heard the door to my room, which lay on the other side of my hiding spot, open softly. Someone entered [and] sat down on a small bench [and] began to read, not loud but quite softly. It was Kramers. Earlier he had lent me a volume of Bradley's 'Lectures on Shakespeare'. What this good man was doing now was reading to me from that book in order to calm my nerves.Later Pais was captured by the Germans and Kramers wrote to Heisenberg asking him to intercede on Pais' behalf.
After World War II, Kramers was elected as chairman of the technical subcommittee of the UN Official International Atomic Energy Commission. He also organized the building of a nuclear reactor using Dutch uranium and Norwegian heavy water, and he was one of the main players in the establishment of the Foundation for Fundamental Research on Matter.
Kramers received many honours for his outstanding contributions, and had he not died at a young age he would certainly have received further honours. Among those he received were the Lorentz Medal (1947), the Hughes Medal (1951) as well as election to the Danish Academy of Sciences and the Royal Dutch Academy of Sciences. He also served as president of the International Union of Pure and Applied Physics and as a member of the board of the Solvay Conferences. Also in 1975 the University of Utrecht founded the Kramers Chair for Theoretical Physics. The first to hold this Chair was Eugene P Wigner.
Pais, writing in , gives this insight into Kramers' character:-
My talks with Kramers showed him to be a man of quite unusual depth in his thinking, not only on physics but also in regard to numerous other aspects of human culture. He was very musical and ... played the cello very well. I remember a story he once told me about music. One evening he was attending a concert of music he was particularly fond of. Suddenly, in the middle of it all, he got up and left, because, he told me, he had found himself sitting there calculating in his head the energy levels of an oxygen atom, unable to concentrate on the music at the same time. That was too much for him. He never went to a concert again but continued to make his own music because that he could do with undivided attention.
Article by: J J O'Connor and E F Robertson