Spectral and scattering theory for the Schrödinger operators with penetrable wall potentials

Ikebe, Teruo; Shimada, Shin-ichi

doi:10.1215/kjm/1250519902

Cited by 18 publications

(11 citation statements)

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“…Applications to higher dimensional singular interactions such as line and surface interactions considered in, e.g., [10], [26], [28], [6] will be discussed in [22] and other future investigations.…”

Section: Introductionmentioning

confidence: 99%

Resolvent formulas of general type and its application to point interactions

Kuroda

Nagatani

2001

J.evol.equ.

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Kiselev and Simon ([13]) considered rank one singular perturbations of general type and formulate such perturbation in terms of a resolvent formula. In an attempt to generalize it beyond the rank one case, it is found that this expression in its generality describes resolvents of a rather wide class of closed operators (or all selfadjoint operators). Bounded operators from the domain of unperturbed operator with the graph norm to its dual space will serve as a parameter. As an application point interactions in one-dimension will be discussed systematically, recapturing selfadjoint boundary conditions associated to the problem.

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Section: Introductionmentioning

confidence: 99%

Resolvent formulas of general type and its application to point interactions

Kuroda

Nagatani

2001

J.evol.equ.

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] For example, it is by now standard to define a Hamiltonian with singular interaction ͑␦, ␦Ј, ␦, and ␦Ј on a sphere, ...͒ by the von Neumann theory of self-adjoint extensions and Krein formula ͑see the review volume of Albeverio et al 2 ͒. The physical motivation 3 comes mainly from nuclear physics where the model introduced by Green and Moszkowski 19 under the name SDI ͑surface delta interaction͒ has been popular.…”

Section: Introductionmentioning

confidence: 99%

Relativistic scattering theory for a δ sphere plus a Coulomb interaction with boundary conditions of second type

Avossevou

Hounkonnou

2000

Journal of Mathematical Physics

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We study stationary relativistic scattering theory for a ␦-sphere interaction formally given by the Hamiltonian HϭH D ϩ␣␦(͉x គ ͉ϪR), x គ R 3 , ␣R, RϾ0 with the boundary conditions of second type. First we give the mathematical definition of the model, self-adjointness of the Hamiltonian, indicial equation, stationary scattering theory and the spectral properties. Next we extend the model by adding a Coulomb potential and provide useful mathematical definitions and corresponding stationary scattering elements.

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“…1. Some of these techniques have recently been used by a number of authors [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] to perform a systematic study of new exactly solvable models of sphere interactions in nonrelativistic quantum mechanics. Except for the recent works, [16][17][18] this is not the case for the relativistic quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Exactly solvable models of δ′-sphere interactions in relativistic quantum mechanics

Hounkonnou

Avossevou

2000

Journal of Mathematical Physics

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A. Characterization of the modelLet us consider in relativistic quantum mechanics and in physical three dimensions a neutral particle of mass M under the influence of ␦Ј-sphere interactions supported by a finite set of N concentric spheres of radii R m ; 1рmрN.The quantum Hamiltonian describing formally this system then reads a͒ Electronic mail: hounkon@syfed.bj.refer.org JOURNAL OF MATHEMATICAL PHYSICS Exactly solvable models of ␦Ј-sphere . . . This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.120.242.61 On: Thu, 27 Nov 2014 04:24:48 2 ͓g jl ͑ k,R mϩ ͒ϩg jl ͑ k,R mϪ ͔͒ϪB m , B m 0 g jl 1720

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Spectral and scattering theory for the Schrödinger operators with penetrable wall potentials

Cited by 18 publications

References 0 publications

Resolvent formulas of general type and its application to point interactions

Resolvent formulas of general type and its application to point interactions

Relativistic scattering theory for a δ sphere plus a Coulomb interaction with boundary conditions of second type

Exactly solvable models of δ′-sphere interactions in relativistic quantum mechanics

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