For many problems in the electron theory of metals none of the methods hitherto used to calculate the eigenfunctions and energy values of an electron in a crystal lattice is satisfactory. It is here proposed that these wave functions and energies be calculated by solving a secular equation with wave functions ${\chi }_k$ which are simply plane waves made orthogonal to the core eigenfunctions. The rapidity of convergence to be expected for such a procedure is discussed. Some methods for practical computation are suggested, and expressions are given for the matrix elements occurring in the secular equation.

• Received 8 April 1940

DOI:https://doi.org/10.1103/PhysRev.57.1169