Numerical calculation of the discrete spectra of one‐dimensional Schrödinger operators with point interactions. (27th December 2018)

• Record Type: Journal Article
• Authors: Barrera‐Figueroa, Víctor; Rabinovich, Vladimir S.
• Other Names: Kravchenko Vladislav V. guestEditor.; Porter R. Michael guestEditor.; Torba Sergii M. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 15(2019)
• Page Start: 5072
• Page End: 5093
• Publication Date: 2018-12-27
• Subjects: δ‐ and δ′‐interactions -- associate functions in the Jordan chain -- complex eigenvalues -- nonself‐adjoint problems -- point interactions -- spectral parameter power series (SPPS) method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5444
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider one‐dimensional Schrödinger operators S q on R with a bounded potential q supported on the segment h 0, h 1 and a singular potential supported at the ends h 0, h 1 . We consider an extension of the operator S q in L 2 R defined by the Schrödinger operator H q = − d 2 d x 2 + q and matrix point conditions at the ends h 0, h 1 . By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator H q . Moreover, we provide closed‐form expressions for the eigenfunctions and associate functions in the Jordan chain given in the form of power series of the spectral parameter. The validity of our approach is proven in several numerical examples including self‐adjoint and nonself‐adjoint problems involving general point interactions described in terms of δ ‐ and δ ′ ‐distributions.