Two-Body Scattering in (1 + 1) Dimensions by a Semi-relativistic Formalism and a Hulthén Interaction Potential

Hassanabadi, S.; Ghominejad, M.; Thylwe, Karl‐Erik

doi:10.1088/0253-6102/63/4/423

Cited by 9 publications

(12 citation statements)

References 51 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The applicability of Hulthén potential led to its modifications by various researchers in relativistic and non-relativistic quantum mechanics [11][12][13][14][15][16][17][18][19] while different approaches have been employed in studying the above mentioned cases.…”

Section: Introductionmentioning

confidence: 99%

The scattering phase shifts of the Hulthén-type potential plus Yukawa potential

Oyewumi

Oluwadare

2016

Eur. Phys. J. Plus

View full text Add to dashboard Cite

The Hulthén-type potential is perturbed by adding Yukawa potential. By applying a short-range approximation to the Schrödinger equation containing this model via standard method, the scattering state solutions and the corresponding phase shifts were obtained. Our numerical calculations and graphical solutions show the dependencies of scattering phase shifts on Yukawa potential constant , asymptotic wave number , screening parameter and angular momentum quantum number .

show abstract

Section: Introductionmentioning

confidence: 99%

The scattering phase shifts of the Hulthén-type potential plus Yukawa potential

Oyewumi

Oluwadare

2016

Eur. Phys. J. Plus

View full text Add to dashboard Cite

show abstract

“…As → −∞ in the region ( < 0) the wave function is the sum of the incident wave and the reflected wave and is of the type [17,18,20,21] ψ ( ) = 1 (1 − ) 2 1 ( , ; ; )…”

Section: The Reflection and Transmission Coefficientsmentioning

confidence: 99%

“…Since no wave is reflected from the region > 0, we thus set the constant 3 to zero in Eq. (15) and have [17,18,20,21] ψ ( ) = 4 − (1 − ) 2 1 (̃+ 1 −̃,̃+ 1 −̃; 2 −̃; ).…”

Section: The Reflection and Transmission Coefficientsmentioning

confidence: 99%

See 1 more Smart Citation

Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng–Fan Potential

Oluwadare¹,

Oyewumi²,

Thylwe³

et al. 2017

Commun. Theor. Phys.

View full text Add to dashboard Cite

By applying continuity and boundary conditions, the reflection and transmission coefficients of one-dimensional time-independent Schrödinger equation with a symmetric IntroductionThe scattering phenomena, such as scattering phase shifts, reflection and transmission coefficients are used to explain the behaviour of waves incident on a barrier [1-2]. The transmission coefficient represents the probability flux of the transmitted wave relative to that of the incident wave. It is often used to describe the probability of a particle tunneling through a barrier. This is more feasible in the case where electrons tunnel between two conducting materials. The shifted Deng-Fan potential is a suitable model for the theoretical predictions because it has been used extensively in both relativistic and non -relativistic quantum mechanics. The original Deng-Fan molecular potential has the correct asymptotic behaviour at the origin [3][4][5][6][7][8][9], and so, it has been used to predict the interactions between atoms and molecules and vibrational spectrum [3][4][5][6][7][8][9].

show abstract

“…[3−4] Most of these applications focus on bound states in (1+1) dimensions (D) and in (1+3)-D. A couple of applications are related to scattering problems, see Refs. [4][5] for (1+1)-D barrier-type interaction potentials. However, early applications to bound and scattering states do not discuss two-body effects, but rather analytic solution methods for specific potential shapes.…”

Section: Introductionmentioning

confidence: 99%

Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods–Saxon Barrier Potential

Thylwe¹

2017

Commun. Theor. Phys.

View full text Add to dashboard Cite

A local momentum (LM) approximation applicable to semi-relativistic two-body repulsive interactions is presented. It assumes negligible variations in the (vector-type) potential. A Woods-Saxon barrier with a rectangularlike shape is studied in some detail. The LM-approximation gives exact results within the semi-relativistic framework for rectangular barrier interactions in (1+1) dimensions. Further approximations of the local momentum approach leads to the two-body approximation of Ikhdair & Sever, known since the early 90's as the spinless Salpeter equation approximating the Bethe-Salpeter equation. LM-and GS-results indicate significant two-body effects. Results obtained from the (single-mass) Dirac equation are similar for certain two-body mass combinations.

show abstract

Two-Body Scattering in (1 + 1) Dimensions by a Semi-relativistic Formalism and a Hulthén Interaction Potential

Abstract: Scattering solutions of two-body Spinless Salpeter Equation (SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulthén potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.

Cited by 9 publications

References 51 publications

The scattering phase shifts of the Hulthén-type potential plus Yukawa potential

The scattering phase shifts of the Hulthén-type potential plus Yukawa potential

Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng–Fan Potential

Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods–Saxon Barrier Potential

Contact Info

Product

Resources

About