Analytical treatment of a two-level system with transitive and displacive vibronic coupling

Abstract

The eigenvalue problem of a Hamiltonian which has been used as a model in exciton dynamics and in the theory of nonradiative transitions is formulated in Bargmann's Hilbert space of analytical functions (1962). For particle combinations of the parameters of the Hamiltonian one finds exact solutions which are elementary transcendental functions. In the general case the eigenvalues and the eigenfunctions are determined by matrix continued fractions. The eigenfunctions can be represented accurately by Neumann expansions with very few terms.