Limit‐point / limit‐circle classification of second‐order differential operators arising in PT quantum mechanics. Issue 1 (October 2016)

• Record Type: Journal Article
• Authors: Büttner, Florian; Trunk, Carsten
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 871
• Page End: 872
• Publication Date: 2016-10
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610424
• Languages: English
• ISSNs: 1617-7061

Abstract

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)