Schrödinger operators with fairly arbitrary spectral features

Krishna, M. ; Sunder, V. S. (1997) Schrödinger operators with fairly arbitrary spectral features Reviews in Mathematical Physics, 9 (3). pp. 343-360. ISSN 0129-055X

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It is shown, using methods of inverse-spectral theory, that there exist Schrödinger operators on the line with fairly general spectral features. Thus, for instance, it follows from the main theorem, that if Σ is any perfect subset of (-∞, 0], then there exist potentials qj, j=1, 2 such that the associated Schrödinger operators Hj are self-adjoint and satisfy: σ(Hj)=Σ∪[0, ∞), σac(Hj)=[0, ∞), σpp(H1)=σsc(H2) =Σ. The main result also implies the existence of states with interesting transport properties.

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