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arXiv · 2504.16123

The DKP Equation in Presence of a Woods-Saxon Potential: Transmission Resonances and Bound States

Alexis Garzón·Ricardo Fernández·Vicente A. Arévalo·David Laroze·Laura M. Pérez·Benjamín de Zayas·Clara Rojas
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Abstract

In this article, we solve the Duffin-Kemmer-Petiau (DKP) equation in the presence of the Woods-Saxon potential barrier and well for spin-one particles. We derive the scattering solution in terms of the Gaussian hypergeometric function ${}_2F_1(a, b; c; z)$, the regularized Gaussian hypergeometric function ${}_2\tilde{F}_1(a, b; c; z)$, and the Gamma function $\Gamma(x)$. Our analysis reveals the presence of transmission resonances. To observe these resonances, we calculate and plot the transmission $T$ and reflection $R$ coefficients for various parameters of the Woods-Saxon potential barrier. Our results are compared with those obtained for the square potential barrier and the cusp potential barrier, which represent limiting cases of the Woods-Saxon potential barrier. Furthermore, we investigate the bound state solutions, determining the critical turning point $V_{cr}$ to study particle-antiparticle creation and compute the norm $N$. Finally, we also compare our results with those obtained for the square potential well and the cusp potential well, confirming that pair creation occurs in both potential wells.

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Alexis Garzón, Ricardo Fernández, Vicente A. Arévalo, David Laroze, Laura M. Pérez, Benjamín de Zayas, Clara Rojas. 2025-04-19. The DKP Equation in Presence of a Woods-Saxon Potential: Transmission Resonances and Bound States. https://arxiv.org/abs/2504.16123

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