Half-Bound States and Levinson’s Theorem for Discrete Systems

1991 ◽  
Vol 22 (3) ◽  
pp. 754-768 ◽  
Author(s):  
D. B. Hinton ◽  
M. Klaus ◽  
J. K. Shaw
Keyword(s):  
Bound States ◽  
Discrete Systems ◽  
Levinson’S Theorem

Levinson's theorem and Titchmarsh-Weyl m(λ) theory for Dirac systems*

1988 ◽  
Vol 109 (1-2) ◽  
pp. 173-186 ◽  
Author(s):  
D. B. Hinton ◽  
M. Klaus ◽  
J. K. Shaw
Keyword(s):  
Asymptotic Behaviour ◽  
Bound States ◽  
Dirac System ◽  
Levinson’S Theorem ◽  
Dirac Systems ◽  
Levinson Theorem ◽  
Asymptotic Phase

SynopsisA Levinson theorem is proved for a Dirac system with one singular endpoint. The number ofbound state is expressed in terms of the change in asymptotic phase of an appropriate solution and in terms of factors whose values depend on the presence of half-bound states. The behaviour of the asymptotic phase is used to determine the asymptotic behaviour of the Titchmarsh-Weyl m-function.

The S-Matrix and Its Analysis

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Acoustic Waves ◽  
Bound States ◽  
Scattering Matrix ◽  
Infinite Dimensional ◽  
Levinson’S Theorem ◽  
S Matrix ◽  
Radial Schrödinger Equation ◽  
Square Well ◽  
Watson Transform ◽  
Remote Past

This chapter focuses on the scattering matrix, or S-matrix, an infinite-dimensional matrix or operator that expresses the state of a scattering system consisting of waves or particles or both in the far future in terms of its state in the remote past. In the case of electromagnetic (or acoustic) waves, the S-matrix connects the intensity, phase, and polarization of the outgoing waves in the far field at various angles to the direction and polarization of the beam pointed toward an obstacle. The chapter first considers the problem of scattering by a square well, located symmetrically with respect to the origin, before discussing bound states and a heuristic derivation of the Breit-Wigner formula. It als describes the Watson transform and Regge poles before concluding with an analysis of the time-independent radial Schrödinger equation and Levinson's theorem.

Bound states and Levinson's theorem for a class of non-local potentials (s-wave)

1968 ◽  
Vol 113 (3) ◽  
pp. 625-640 ◽  
Author(s):  
M. Bertero ◽  
G. Talenti ◽  
G.A. Viano
Keyword(s):  
Bound States ◽  
S Wave ◽  
Levinson’S Theorem ◽  
Non Local ◽  
Local Potentials

Recent Radiative and Collisional Atomic Data of Astrophysical Interest

1988 ◽  
Vol 102 ◽  
pp. 129-132
Author(s):  
K.L. Baluja ◽  
K. Butler ◽  
J. Le Bourlot ◽  
C.J. Zeippen
Keyword(s):  
Mass Production ◽  
Bound States ◽  
Physical Models ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Isoelectronic Sequence ◽  
Astrophysical Interest ◽  
Radiative Transitions ◽  
Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

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