Bivariational methods applied to Schrodinger's and Dirac's equations

Abstract

A class of bivariational functionals is derived whose stationary points are pairs of solutions of the single-particle Schrodinger equation (or Dirac equation, respectively) subject to so-called 'complementary boundary conditions'. The formulation of the boundary value problem is sufficiently general to include matching conditions and Bloch conditions as well as scattering conditions. It is shown how bivariational translational techniques may be applied to problems with three- and two-dimensional translational symmetry (calculation of complex band structures and propagation matrices, scattering problems).