This research demonstrates how energy-dependent potentials affect scattering and reflection in the DKP equation, indicating the significance of smooth barriers.
In this work, we investigate the Duffin--Kemmer--Petiau (DKP) equation in the presence of smooth, barrier-type energy-dependent potentials (EDPs) in (1 + 1)-dimensional space-time. The eigenfunctions are obtained in terms of the confluent Heun function HeunC(α, β, γ, δ, ε, y), and a well-defined expression is derived for the spectrum. The transmission and reflection coefficients are calculated and a numerical analysis of these coefficients is presented for specific values of the parameters V₀ and E. A comparison is made between the cases where the potential is energy-dependent (ρ ≠ 0) and energy-independent (ρ = 0).
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Langueur et al. (2025) studied this question.
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