Schrödinger Operators with Decaying Potentials : Some Counterexamples

  title={Schr{\"o}dinger Operators with Decaying Potentials : Some Counterexamples},
  author={Christian Remling},
More specifically, we study the spectral properties of the associated selfadjoint operatorsHβ = −d2/dx2+ V (x), acting on the Hilbert space L2(0,∞). The index β ∈ [0,π) refers to the boundary condition y(0)cosβ + y′(0)sinβ = 0. For the general theory, see, for example, [29]. These questions are of relevance in quantum mechanics; for more background information on this topic, refer to, for example, [18]. SinceV tends to zero asx →∞, it follows that the essential spectrum satisfies σess= [0… CONTINUE READING