Convergence of an exact quantization scheme

Details Convergence of an exact quantization scheme Convergence of an exact quantization scheme

2003-06-13

arxiv.org/abs/math/0306218v1

Mathematics

Dynamical Systems

10 pages, no figures, first version

Scientific paper

10.1007/s00220-004-1112-9

It has been shown by Voros \cite {V} that the spectrum of the one-dimensional
homogeneous anharmonic oscillator (Schr\"odinger 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.

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