Benjamín de Zayas | Searcharxiv

arXiv2026

Study of the Superradiance Phenomenon in the $α$--attractor Potential using the Log Derivative Method

In this article, we solved the time--independent one--dimensional Klein--Gordon equation in the presence of $α$--attractor potential using the Log derivative method. We calculated the reflection coefficient $\mathcal{R}$ and the transmission coefficient $\mathcal{T}$, showing that the superradiance phenomenon is present. In order to demonstrate the accuracy of our method, we performed a comparison with the analytical solution for the hyperbolic tangent potential.

quant-ph↗

arXiv2025

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

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 $Γ(x)$. 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.

quant-ph↗