We obtain the rigorous WKB expansion to all orders for the radial Kepler problem, using the residue calculus in evaluating the WKB quantization condition in terms of a complex contour integral in the complexified coordinate plane. The procedure yields the exact energy spectrum of this Schrödinger eigenvalue problem and thus resolves the controversies around the so-called ”Langer correction”. Th...

We derive a determinant formula for the WKB exponential of singularly perturbed Zakharov-Shabat system that corresponds to the semiclassical (zero dispersion) limit of the focusing Nonlinear Schrödinger equation. The derivation is based on the RiemannHilbert Problem (RHP) representation of the WKB exponential. We also prove its independence of the branchpoints of the corresponding hyperelliptic...

We consider coordinate systems adapted to accelerated observers, construct a generalised Rindler metric and then adopt a specific form of it to compute the semiclassical Unruh temperature, using a WKB approximation within a Hamilton Jacobi analysis in the tunneling picture. Corrections to this temperature are next computed by going beyond the usual WKB approximation. A connection of the correct...