Any theoretical physicist has met, in his introduction to the subject, the simplest examples of Schrödinger's equation, including the harmonic oscill… - Rudolf Peierls

At about this same time Dirac wrote a paper that proposed a general theory of how measurements should be described in quantum mechanics. Similar work was also done by P. Jordan in Göttingen. These two papers constitute what is called transformation theory, because they show how one can transform information gained by measuring one quantity into predicting information about another.

With both light and electrons, one was faced with the so-called "wave-particle duality"; both could be regarded as waves for some purposes and as particles for others. An important step in resolving this paradox was a paper by Max Born in July 1926, in which he suggested that the waves determine the probability of finding the particle in a particular place. This idea was already considered much earlier by Einstein, but it was rejected by him. This interpretation of the theory was further developed in the spring of 1927 by Heisenberg, who formulated his "uncertainty principle" ...

His contributions to condensed matter physics were largely on fundamental questions, establishing the principles of this subject. Most of this work was done during the years 1928–37, but much of it could not be tested until the experimental techniques needed for this had become sufficiently developed. ...
Rudolf Peierls's work in nuclear physics began in 1933, when James Chadwick challenged him and Hans Bethe to explain his first measurements of the cross-section for photo-disintegration of the deuteron. Peierls's experience in this field developed rapidly within the next few years, on both practical questions and academic research, to the point where he and Otto Frisch could confidently conclude that the construction of an atomic bomb would be quite possible using ²³⁵U, which could be obtained obtained from natural uranium by a feasible separation process, and they pointed this out in the famous Frisch-Peierls Memorandum of 1940 which they sent to the British government. This led to the Atomic Bomb Project, at first in Britain under the name "Tube Alloys Project" and later in USA as the "Manhattan District Project", which many of the UK scientists, including both Peierls and Frisch, were sent to join at the end of 1943.