One-dimensional Schrödinger operators with ergodic potential (Q788398)

In the first part of the paper the results by J. M. Luttinger, L. Dworin and H. Matsuda concerning the following problem of G. Saxon and G. Hutner are generalised: Which conditions guarantee that an energy value E lies in the resolvent set of the Hamiltonian for an alloy, presupposing that E lies in the resolvent set of the Hamiltonians of all pure components. The extension of the trapping region even yields necessary conditions as will be shown in another author's paper. In the third part the ground-state energy is investigated for different types of the ergodic potential. For comparison, examples with almost periodic potentials are given. E.g. Gordon's result concerning eigenvalues for such operators is generalised in the second part.