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<p>In this work, we study the Duffin–Kemmer–Petiau (DKP) equation in space-time dimensions (1 + 2) in the presence of scalar and vector electromagnetic of hyperbolic tangent form. The eigenfunctions are determined as a function of the hypergeometric function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F(\alpha ,\beta ;\upgamma ;z)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>;</mo> <mi mathvariant="normal">γ</mi> <mo>;</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Special cases such as linear potential and step potential are analyzed where the transmission and reflection coefficients are calculated as well as the Klein’s paradox region has been analyzed and persisted. A numerical study is presented for the graphs of the transmission and reflection coefficients as well as the energy spectrum for certain values of the parameters (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(E_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(H_{0},a\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>a</mi> </mrow> </math></EquationSource> </InlineEquation>) are plotted.</p>

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DKP Equation with a Mixing of Hyperbolic Tangential Electromagnetic Field Vector and Scalar Potentials

  • 期刊论文

  • 发表日期：

    2026年2月20日

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  • O. Langueur,
  • M. Merad

摘要

In this work, we study the Duffin–Kemmer–Petiau (DKP) equation in space-time dimensions (1 + 2) in the presence of scalar and vector electromagnetic of hyperbolic tangent form. The eigenfunctions are determined as a function of the hypergeometric function \(F(\alpha ,\beta ;\upgamma ;z)\) F ( α , β ; γ ; z ) . Special cases such as linear potential and step potential are analyzed where the transmission and reflection coefficients are calculated as well as the Klein’s paradox region has been analyzed and persisted. A numerical study is presented for the graphs of the transmission and reflection coefficients as well as the energy spectrum for certain values of the parameters ( \(E_{0}\) E 0 , \(H_{0},a\) H 0 , a ) are plotted.