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1
Content available remote

Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

100%
Wei G.-F., Qiang W.-C., Chen W.-L.
Open Physics
|
2010
|
vol. 8
|
issue 4
574-579
EN
The continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.
2
Content available remote

Proposal to improve the behaviour of self-energy contributions to the S-matrix

76%
Tóth G.
Open Physics
|
2010
|
vol. 8
|
issue 4
527-541
EN
A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.
3
Content available remote

Asymptotics of Resonances Induced by Point Interactions

76%
Lipovský J., Lotoreichik V.
Acta Physica Polonica A
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2017
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vol. 132
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issue 6
1677-1682
EN
We consider the resonances of the self-adjoint three-dimensional Schrödinger operator with point interactions of constant strength supported on the set X={xₙ}_{n=1}^{N}. The size of X is defined by V_{X} = max_{π ∈ Π_{N}} ∑_{n=1}^{N} |xₙ - x_{π(n)}|, where Π_{N} is the family of all the permutations of the set {1,2,...,N}. We prove that the number of resonances counted with multiplicities and lying inside the disc of radius R behaves asymptotically linear W_{X}/πR + O(1) as R → ∞, where the constant W_{X} ∈ [0,V_{X}] can be seen as the effective size of X. Moreover, we show that there exist a configuration of any number of points such that W_{X}=V_{X}. Finally, we construct an example for N=4 with W_{X} < V_{X}, which can be viewed as an analogue of a quantum graph with non-Weyl asymptotics of resonances.
4
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Transmission resonance for a Dirac particle in a one-dimensional Hulthén potential

76%
Guo J., Yu Y., Jin S.
Open Physics
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2009
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vol. 7
|
issue 1
168-174
EN
We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have derived the reflection and transmission coefficients using the matching condition on the wavefunctions, and investigated the condition for the existence of transmission resonance. Furthermore, we have demonstrated how the transmission resonance depends on the shape of the potential.
5
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The Elastic Collision of Two H-Like Atoms Including the Exotic Ps and Mu

76%
Ray H.
Acta Physica Polonica A
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2017
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vol. 132
|
issue 5
1473-1477
EN
Elastic collision between two H-like atoms using the ab initio static-exchange model (SEM) and a modified static-exchange model (MSEM) at cold energies are investigated in the center of mass frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. The importance of an exact calculation to find basic physics is highlighted. In addition, the dependence of scattering length on the van der Waals interaction between the atoms and the dependence of scattering length on reduced-mass of the system are derived which is completely new information in the field of science.
6
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Fluctuations and Correlations in Scattering on a Resonance Coupled to a Chaotic Background

64%
Savin D.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 6
1688-1694
EN
We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the presence of a complex environment. Using a statistical model based on random matrix theory, we obtain a number of nonperturbative results for various statistics of scattering characteristics. This includes the joint and marginal distributions of the reflection and transmission intensities and phases, which are derived exactly at arbitrary coupling to the background with finite absorption. The intensities and phases are found to exhibit highly non-trivial statistical correlations, which remain essential even in the limit of strong absorption. In the latter case, we also consider the relevant approximations and their accuracy. As an application, we briefly discuss the statistics of the phase rigidity (or mode complexness) in such a scattering situation.
7
Content available remote

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

64%
Wei G.-F., Zhen Z.-Z., Dong S.-H.
Open Physics
|
2009
|
vol. 7
|
issue 1
175-183
EN
The approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for wave is studied briefly.
8
Content available remote

The propagator for step potential and mass using path decomposition method

64%
Laissaoui A., Chetouani L.
Open Physics
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2010
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vol. 8
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issue 4
562-573
EN
The one-dimensional path decomposition expression for the step potential and mass is formulated. The propagator is analytically determined and the limiting case m 1; m 2 → m is exactly obtained.
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