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… - Rudolf Peierls

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.

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.

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.