Born approximation is a familiar and convenient approximation in handling scattering problems. It is adequate, or at least informative, in so many ca… - Rudolf Peierls

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.

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.