Airy function (exact WKB results for potentials of odd degree) (2007)
] H def = \Gamma d 2 dq 2 + q N ; for N an even integer. (1) (Obvious dependences upon the parameter N will be left implied.) Over L 2 (R), H is a strictly positive operator; it has a purely discrete...
A sharpening of Li's criterion for the Riemann Hypothesis (2006)
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true,...
The general 1D Schr\"odinger equation as an exactly solvable problem (2006)
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented...
From exact-WKB towards singular quantum perturbation theory (2006)
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M...
From exact-WKB toward singular quantum perturbation theory II (2006)
Following earlier studies, several new features of singular perturbation theory for one-dimensional quantum anharmonic oscillators are computed by exact WKB analysis; former results are thus...
Sharpenings of Li's criterion for the Riemann Hypothesis (2005)
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is...
The general 1D Schr\"odinger equation as an exactly solvable problem (2004)
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented...
A sharpening of Li's criterion for the Riemann Hypothesis (2004)
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true,...
From exact-WKB towards singular quantum perturbation theory (2004)
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schrödinger eigenvalue problems on the real line with polynomial potentials of the form...
A sharpening of Li's criterion for the Riemann Hypothesis (2004)
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true,...
The general 1D Schr\"odinger equation as an exactly solvable problem (2004)
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented...
A sharpening of Li's criterion for the Riemann Hypothesis (2004)
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true,...
The general 1D Schr\"odinger equation as an exactly solvable problem (2004)
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented...
From exact-WKB towards singular quantum perturbation theory (2003)
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M...
From exact-WKB towards singular quantum perturbation theory (2003)
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M...
From exact-WKB towards singular quantum perturbation theory (2003)
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M...
An exact solution method for 1D polynomial Schrödinger equations (1999)
André Voros, Schrodinger Equations
Stationary 1D Schrodinger equations with polynomial potentials are reduced to explicit countable closed systems of exact quantization conditions, which are selfconsistent constraints upon the zeros...