Characterization of one-dimensional point interactions for the Schrodingeroperator by means of boundary conditions

Authors
Brzezniak, Z Jefferies, B
Citation
Z. Brzezniak et B. Jefferies, Characterization of one-dimensional point interactions for the Schrodingeroperator by means of boundary conditions, J PHYS A, 34(14), 2001, pp. 2977-2983
Citations number
16
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
14
Year of publication
2001
Pages
2977 - 2983
Database
ISI
SICI code
0305-4470(20010413)34:14<2977:COOPIF>2.0.ZU;2-U
Abstract
We find a new representation of all boundary conditions corresponding to th e so-called point interactions. We show that there is one-to-one correspond ence between one-dimensional point interactions and boundary conditions of the form u'(0(+))+ iu(0(+)) = eta alpha (u'(0(+)) - iu((0(+))) - eta<(<beta>)over ba r>(u'(0(-)) + iu(0(-))) u'(0(-)) - iu(0(-)) = eta beta (u'(0(+)) - iu(0(+))) + eta<(<alpha>)over ba r>(u'(0(-)) + iu(0(-))) with alpha, beta, eta is an element of C satisfying \eta\ = \alpha\(2) + \b eta\(2) = 1.