On a class of Sturm‐Liouville operators which are connected to PT symmetric problems. Issue 1 (December 2014) - Azizov, Tomas Ya.; Trunk, Carsten
Abstract A prominent class of <alternatives> <![CDATA[$\cal PT$]]> <inline-graphic xlink:href="ark:/27927/pgh2xqgcn30" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /></alternatives> ‐symmetric Hamiltonians is <alternatives> <![CDATA[$H := {1\over2} p^2 + x^2(ix)^N, \quad {\rm for\ } x\in\Gamma$]]> </alternatives> for some nonnegative number N. The associated eigenvalue problem is defined on a contour Γ in a specific area in the complex plane (Stokes wedges), see [3, 5]. In this short note we consider the case N=2 only. Here we elaborate the relationship between Stokes lines and Stokes wedges and well‐known limit point/limit circle criteria from [6, 10, 11]. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)