2,016 research outputs found
Convergence of an exact quantization scheme
It has been shown by Voros \cite {V} that the spectrum of the one-dimensional
homogeneous anharmonic oscillator (Schr\"odinger operator with potential
, ) is a fixed point of an explicit non-linear transformation. We
show that this fixed point is globally and exponentially attractive in spaces
of properly normalized sequences.Comment: 10 pages, no figures, first versio
Generic singular spectrum for ergodic Schrödinger operators
We consider Schrödinger operators with ergodic potential V_ω(n) = f(T^n(ω)), n Є Z, ω Є Ω, where T : Ω → Ω is a nonperiodic homeomorphism. We show that for generic f Є C(Ω), the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani theory
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