Communications in Mathematical Physics

, Volume 158, Issue 2, pp 315–325 | Cite as

Internal Lifschitz singularities for one dimensional Schrödinger operators

  • G. A. Mezincescu


The integrated density of states of the periodic plus random one-dimensional Schrödinger operator\(H_\omega = - \Delta + V_{per} + \sum\limits_i {qi\left( \omega \right)f\left( {o - i} \right)} \);f≥0,q i (ω)≥0, has Lifschitz singularities at the edges of the gaps inSp(Hω). We use Dirichlet-Neumann bracketing based on a specifically one-dimensional construction of bracketing operators without eigenvalues in a given gap of the periodic ones.


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© Springer-Verlag 1993

Authors and Affiliations

  • G. A. Mezincescu
    • 1
  1. 1.Institut für MathematikRuhr-Universität BochumGermany

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