Kovaˇrík: Spectrum of the Schrödinger operator in a perturbed periodically twisted tube

Abstract. We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of “slowing down ” the twisting in the mean gives rise to a non-empty discrete spectrum. Mathematics Subject Classification: 35P05, 81Q10. Key words. Schrödinger operator, discrete spectrum, twisting