Nonadiabatic Electron–Phonon Interaction. Matrix Continued Fraction Treatments and Reduction of High‐Dimensional Problems

Abstract

AbstractAn electronic two‐level system interacting with two different vibrational modes via displacive and transitive couplings is investigated. The eigensolutions are determined using a matrix continued fraction method including infinite matrices. The approximations used in the numerical evaluation are discussed. As another example for the applicability of the continued fraction method it is shown that the E–e‐Jahn‐Teller Hamiltonian proves to be a specialized case, whose eigenvalue problem may be solved using ordinary continued fractions. Finally, the eigenvalue problem of the extended Hubbard Hamiltonian of a dimer with linear local electron–phonon coupling is reduced to the evaluation of a matrix continued fraction with three‐dimensional matrices.