A Mathematical Model of Heavy-Quarkonia Mesonic Decays

Antoine, Jean-Pierre; Exner, Pavel; Šeba, P.; Shabani, Juma

doi:10.1006/aphy.1994.1058

Cited by 19 publications

(14 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As usual in such situations [3,18] the singularities of G ∞ (x, y; k) cancel with those of the added term in (5.2) and the resolvent poles are given by zeros of the denominator (5.5); the exception is represented by the case of an integer or halfinteger φ . For the sake of simplicity, we shall speak mostly about the δ-coupling situation.…”

Section: Pole Trajectoriesmentioning

confidence: 90%

See 1 more Smart Citation

Magnetoresonances on a lasso graph

Exner

1997

Found Phys

View full text Add to dashboard Cite

We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection amplitude and show that there is an infinite ladder of resonances; analyzing the resonance pole trajectories we show that half of them turn into true embedded eigenvalues provided the flux through the loop is an integer or halfinteger multiple of the flux unit hc/e . We also describe a general method to solve the scattering problem on graphs of which the present model is a simple particular case. Finally, we discuss ways in which a state localized initially at the loop decays.I begun my career at times when the world was much less connected, and of most parts we knew only from journals arriving not quite regularly. My first encounter with the mathematical theory of unstable quantum systems and related scattering problems occurred in this way, particularly through [24,25] and related papers by Larry Horwitz; the subject remained for me as well as for him an old love to which we return regularly from time to time. Only many years later I had an opportunity to met him in person and to appreciate also his charisma. A distinguished birthday is a good opportunity to come with another decay scattering system; I should say that I prefer presents which are amusing rather than expensive.

show abstract

Section: Pole Trajectoriesmentioning

confidence: 90%

“…These effects fit well, of course, into the general theory of decay scattering systems as exposed in [10,Chaps. 1,3], [28], or [32,Sec.XII.6], but they also make it possible to illustrate it and to draw fully specific conclusions.…”

Section: Introductionmentioning

confidence: 99%

Magnetoresonances on a lasso graph

Exner

1997

Found Phys

View full text Add to dashboard Cite

show abstract

“…[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

View full text Add to dashboard Cite

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.

show abstract

“…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

View full text Add to dashboard Cite

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

show abstract

A Mathematical Model of Heavy-Quarkonia Mesonic Decays

Cited by 19 publications

References 0 publications

Magnetoresonances on a lasso graph

Magnetoresonances on a lasso graph

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

Contact Info

Product

Resources

About