TY - JOUR
T1 - Numerical calculation of the discrete spectra of one-dimensional Schrödinger operators with point interactions
AU - Barrera-Figueroa, Víctor
AU - Rabinovich, Vladimir S.
N1 - Publisher Copyright:
© 2018 John Wiley & Sons, Ltd.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - In this paper, we consider one-dimensional Schrödinger operators Sq on (Formula presented.) with a bounded potential q supported on the segment [h0, h1] and a singular potential supported at the ends h0, h1. We consider an extension of the operator Sq in (Formula presented.) defined by the Schrödinger operator (Formula presented.) and matrix point conditions at the ends h0, h1. By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator Hq. 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.
AB - In this paper, we consider one-dimensional Schrödinger operators Sq on (Formula presented.) with a bounded potential q supported on the segment [h0, h1] and a singular potential supported at the ends h0, h1. We consider an extension of the operator Sq in (Formula presented.) defined by the Schrödinger operator (Formula presented.) and matrix point conditions at the ends h0, h1. By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator Hq. 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.
KW - associate functions in the Jordan chain
KW - complex eigenvalues
KW - nonself-adjoint problems
KW - point interactions
KW - spectral parameter power series (SPPS) method
KW - δ- and δ′-interactions
UR - http://www.scopus.com/inward/record.url?scp=85059155547&partnerID=8YFLogxK
U2 - 10.1002/mma.5444
DO - 10.1002/mma.5444
M3 - Artículo
SN - 0170-4214
VL - 42
SP - 5072
EP - 5093
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 15
ER -