Rudolf Peierls

"Born approximation is a familiar and convenient approximation in handling scattering problems. It is adequate, or at least informative, in so many cases that we tend to develop the habit of using its first-order term without always checking the conditions for its applicability."

"An important episode for my understanding of conduction problems arose from a paper by Kretschmann, ... who attacked the then accepted theory of conductivity and claimed that the basis of the papers by Bloch and others was quite wrong. He had a number of objections which were mostly not very well conceived, but he claimed, in particular, that in the usual derivation of the Boltzmann equation one had made unjustified use of perturbation theory. In trying to defend the theory I therefore set out to prove that perturbation theory was in order, and to my amazement I found that this was very questionable, if not exactly for the reasons given by Kretschmann. It appeared that the usual application of Fermi's 'golden rule' depended on the inequality ħ/τ ≪ kT, where τ is the collision time. This was not satisfied for many metals. Indeed Landau's dimensional analysis made them comparable. ..."

"Any theoretical physicist has met, in his introduction to the subject, the simplest examples of Schrödinger's equation, including the harmonic oscillator. In demonstrating its solution, it is usually shown that for energies satisfying the usual quantum condition, E = (n + ½)ħω (1.1.1) where n is a non-negative integer and ω the frequency, the equation has a solution satisfying the correct boundary conditions. It is equally important to know that these are the only solutions, i.e., that for an energy not equal to (1.1.1) no admissible solution exists. This negative statement is not usually proved in elementary treatments, or else it is deduced from quite elaborate discussions of the convergence and behavior of a certain infinite series. It is therefore surprising to find that the result can be seen without any complicated algebra."

"The atoms which constitute a solid consist of nuclei and electrons. For a description of the state of the solid it is not, however, necessary to specify the state of all the Z electrons of each atom, since we can eliminate most or all of them by a principle that is familiar from the theory of molecules. ... Since the atomic nuclei are much heavier than the electrons, they move much more slowly, and it is therefore reasonable to start from the approximation in which they are taken to be taken to be at rest, though not necessarily in the regular positions."

"1.4 Types of binding ... The most important types of force are as follows: (a) Electrostatic forces. In an ionic crystal the attraction is mainly due to the Coulomb interaction between point charges. This is particularly amenable to calculation, and a great deal of work has been done on it. The force is a 'two-body' force, i.e. the interaction between two given ions is independent of the positions of any other ions that may be present. ... (b) Van der Waals forces. This name describes the effect that a neutral and isotropic atom can acquire a polarization under the influence of an electric field, and even two neutral isotropic atoms will induce small dipole moments in each other, due to the fluctuating moments which they possess because of the existence of virtual excited states. ... (c) Homopolar binding. These are forces like those effective in homopolar molecules, and we know they are due to the exchange of electrons between the atoms. In molecular crystals (H2, Cl2, etc.) these bonds can easily be localized and we can start from a description of the molecular by the methods of quantum chemistry and then add the relatively weak forces between different molecules. In other cases, however, such as diamond or graphite, each atom shares some valence electrons with each of its neighbors, and it is therefore not possible to single out any given groups of atoms that may be regarded as chemically saturated. The quantitative discussion of such forces is not easy. ... (d) Overlap. If two atoms approach so closely that their electron shells overlap, then there is a strong repulsive force between them. ... (e) Metallic bond. ... it is worth noting that in the case of a metal the presence and motion of the conduction electrons is an important factor in holding the crystal together and in determining its structure."

"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" ..."

"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."

"When I arrived in Leipzig, Heisenberg was working on the theory of ferromagnetism. It was known the magnetism of such substances as iron was due to the "spin" of the electrons inside the substance. Each electron spins like a little top, and in the iron there is a "molecular field", a force that tends to align the spin of each electron with that of its neighbors. But the nature of this field was unknown. It could not be a magnetic effect because magnetic forces are much too weak to account for the observed behaviour. Heisenberg saw that the answer lay in the Pauli exclusion principle, which says that no two electrons can be in exactly the same state. Thus two electrons with the same spin orientation keep out of each other's way; while this repulsion may increase their energy of motion, it diminishes their mutual repulsion, and can therefore lead to a decrease in total energy, making the parallel alignment of the electron spins energetically favourable. He had encountered this mechanism in the theory of atomic spectra and concluded that it was also responsible for ferromagnetism."

"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."

"Richard Dalitz, in: (quote from page v)"

"It is Rudi's genius to show the reader in concrete terms how to do the predicting after some organized thinking."

"After the war, Bethe went back to Cornell, where he helped build an outstanding research center in high-energy physics. Peierls returned to Birmingham, where he created the outstanding school of theoretical physics in Western Europe. The two physicists established a pipeline between the two institutions and offered their generous evaluations of the young postdocs and colleagues—Hugh McManus, Edwin Salpeter, Stuart Butler, Richard Dalitz, Freeman Dyson, and others—that they sent to one another. Their correspondence likewise gives perceptive overviews of advances in high-energy physics, especially of the progress made after 1955 in the nuclear many-body problem on which Bethe was concentrating. Their letters also concern policy challenges posed by, for example, the cold war, nuclear weaponry, nuclear test ban treaties, and antiballistic missiles."