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Communications in Mathematical Physics

, Volume 83, Issue 2, pp 281–302 | Cite as

Stability of Schrödinger eigenvalue problems

  • E. Vock
  • W. Hunziker
Article

Abstract

We derive a general stability criterion for discrete eigenvalues of Schrödinger operators, such asA(κ)=p2+V(x, κ), using only strong continuity ofA(κ) andA*(κ) in the perturbation parameter κ. The theory is developed for non-selfadjoint operators and illustrated with examples like the anharmonic oscillator, the Stark and the Zeeman effect. The principal tools are Weyl's criterion for the essential spectrum and a construction due to Enss [5]. They are also used to extend the classical invariance theorems for the essential spectrum to certain singular perturbations, including some local perturbations of the Laplacian by differential operators of arbitrary high order.

Keywords

Neural Network Differential Operator Quantum Computing Stability Criterion Singular Perturbation 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • E. Vock
    • 1
  • W. Hunziker
    • 1
  1. 1.Institut für Theoretische PhysikETH HönggerbergZürichSwitzerland

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