Convergence of an exact quantization scheme

Abstract

It has been shown by Voros \cite {V} that the spectrum of the one-dimensional homogeneous anharmonic oscillator (Schrödinger operator with potential $q^{2M}$, $M>1$) 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.

10 pages, no figures, first version

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