Iii. Solid State Physics

The application of symmetry considerations to the theory of superconductivity has been considered further. The problem consists of extending the methods recently advanced (1) so as to include the interaction of the electrons with the lattice vibrations. (See Quarterly Progress Report, April 15, 1951.) It now appears that the difficulties which have been blocking progress are not of a formal mathematical, but rather of a conceptual nature. In other words, symmetry considerations may be expected to provide essential qualitative information on the nature of superconductivity, since both the quantum mechanical presentation of electronic currents and the parameters describing transitions of the second kind are closely connected with the translational symmetry of the crystal in question (2). The simple structure of the group of translations is responsible for the mathematical simplicity. The difficulty arises from the traditional way of describing the electronic wave functions of solids as the solutions of the wave equation with a potential energy of fixed periodicity. Not only does this approach lack any quantum mechanical justification, but it actually eliminates the type of wave functions which seem to be required for the description of