The authors construct explicit closed quantization contours encircling the origin for radial Schrödinger problems and use a logarithmic coordinate change to equate closed-cycle and open-connection quantization while incorporating the Maslov phase via renormalization-group arguments.
Convergence behavior of variational perturbation expansion-- A method for locating Bender-Wu singularities
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abstract
Variational perturbation expansions have recently been used to calculate directly the strong-coupling expansion coefficients of the anharmonic oscillator. The convergence is exponentially fast with superimposed oscillations, as recently observed empirically by the authors. In this note, the observed behavior is explained and used to determine accurately the magnitude and phase of the leading Bender-Wu singularity which is responsible for the finite convergence radius in the complex coupling constant plane.
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Exact WKB method for radial Schr\"odinger equation
The authors construct explicit closed quantization contours encircling the origin for radial Schrödinger problems and use a logarithmic coordinate change to equate closed-cycle and open-connection quantization while incorporating the Maslov phase via renormalization-group arguments.