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math.CA2025
Rigorous Methods for Bohr-Sommerfeld Quantization Rules
Joanne Dong, Peter D. Miller, Giorgio Young
In this work, we prove Bohr-Sommerfeld quantization rules for the self-adjoint Zakharov-Shabat system and the Schrödinger equation in the presence of two simple turning points boun…
math.CA2008★ 4 cited
The dbar steepest descent method for orthogonal polynomials on the real line with varying weights
K. T. -R. McLaughlin, P. D. Miller
We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form on the real line, as…