Generalization of the amplitude-phase<i>S</i>-matrix formula for coupled scattering states

Thylwe, Karl‐Erik

doi:10.1088/0305-4470/38/46/007

Cited by 14 publications

(31 citation statements)

References 21 publications

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“…Some details obviously remain to be worked out. The main issue concerns phase-functions for coupled equations, a problem that has already been considered in quantum scattering problems [13]. Hence, we feel very optimistic.…”

Section: Introductionmentioning

confidence: 99%

A characteristic approach to the quasi-normal mode problem

Samuelsson¹,

Andersson²,

Maniopoulou³

2007

Class. Quantum Grav.

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In this paper we discuss a new approach to the quasi-normal mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex valued radial coordinate, we reformulate the standard outgoing-wave boundary condition as a zero Dirichlet condition. This has a number of important advantages over previous strategies. The characteristic formulation permits coordinate compactification, which means that we can impose the boundary condition at future null infinity. The phase function avoids oscillatory behaviour in the solution, and the use of a complex radial variable allows a clean distinction between out-and ingoing waves. We demonstrate that the method is easy to implement, and that it leads to high precision numerical results. Finally, we argue that the method should generalise to the important problem of rapidly rotating neutron star spacetimes. *

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Section: Introductionmentioning

confidence: 99%

A characteristic approach to the quasi-normal mode problem

Samuelsson¹,

Andersson²,

Maniopoulou³

2007

Class. Quantum Grav.

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“…If the effective potential is repulsive in a region containing the origin (see Fig. 1) the amplitude function will increase exponentially [16,17]. This behavior is illustrated in Fig.…”

Section: Methods With One Amplitude Functionmentioning

confidence: 83%

“…Another case is the reflection/transmission solutions in the presence of thick potential barriers [16]; see also [17]. Therefore, like semiclassical representations of the Wentzel-Kramers-Brillouin (WKB) type [16], the amplitude-phase representations of a wave can be seen as 'locally valid' and connections between them are useful in the present study. As yet, connections of 'local' amplitude-phase representations occur only between regions of oscillating waves [15].…”

mentioning

confidence: 99%

“…A typical case is the problem of calculating bound-state solutions and energies in double-well potantials [15]. Another case is the reflection/transmission solutions in the presence of thick potential barriers [16]; see also [17]. Therefore, like semiclassical representations of the Wentzel-Kramers-Brillouin (WKB) type [16], the amplitude-phase representations of a wave can be seen as 'locally valid' and connections between them are useful in the present study.…”

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confidence: 99%

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Heavy-particle resonance phase shifts: an improved amplitude–phase formula

Thylwe

2018

J Math Chem

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An improved amplitude-phase formula suitable for non-relativistic heavyparticle resonance phase shifts is derived. The present formula makes use of two amplitude functions instead of one for a central potential; an inner amplitude which is non-oscillatory in the well region of the effective potential, and an outer amplitude function which is non-oscillatory far away from the origin of the effective potential. The low-energy limit is discussed in connection with Levinson's theorem. Numerical computations at resonance energies and graphical illustrations are presented. Numerical comparisons with an existing single-amplitude formula are made. Keywords Elastic molecular scattering • Resonances • Phase shifts • Amplitude-phase method 1 lntroduction A study of scattering resonances need reliable computations of phase shifts [1-4]. Absolute values of phase shifts with correct multiples of π plays an important role in connection with Levinson's theorem and the correct number of bound states in a given effective potential [2,5], as well as for calculations of virial coefficients [3,4]. Numerical methods and algorithms do not automatically provide phase shifts with correct multiples of π [3,4,6-8], partly because calculations of cross sections do not require correct multiples of π. For use of methods other than amplitude-phase methods, Wei and Le Roy (2006) [3,4] present a quantal/semiclassical method to calculate absolute

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“…where t is the transmission amplitude. The reflection coefficient R and the transmission coefficient T are defined by [7] R = |r| 2 , T = |t| 2 .…”

Section: Scattering Boundary Conditionsmentioning

confidence: 99%

Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

Thylwe

Oluwadare

Oyewumi

2016

Commun. Theor. Phys.

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A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ϵ − V0| < 2µc 2 , where µ is the reduced mass, ϵ the scattering energy, and V0 the barrier top energy. The approximate wave numbers are less accurate.

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Generalization of the amplitude-phaseS-matrix formula for coupled scattering states

Cited by 14 publications

References 21 publications

A characteristic approach to the quasi-normal mode problem

A characteristic approach to the quasi-normal mode problem

Heavy-particle resonance phase shifts: an improved amplitude–phase formula

Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

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