Limit‐point / limit‐circle classification of second‐order differential operators arising in PT quantum mechanics. Issue 1 (October 2016) - Büttner, Florian; Trunk, Carsten
Abstract: We consider a second‐order differential equation − y ″ + q ( x ) y ( x ) = λ y ( x ) with complex‐valued potential q and eigenvalue parameter λ ∈ ℂ. In PT quantum mechanics the potential q is given by q ( x ) = −( ix ) N +2 on a contour Γ ⊂ ℂ. Via a parametrization we obtain two differential equations on [0, ∞) and (−∞, 0]. We give a limit‐point/limit‐circle classification of this problem via WKB‐analysis. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)