Bound states solutions to the DKP equation for the Woods-Saxon potential well

This work focuses on Relativistic Quantum Mechanics (RQM), especially on relativistic wave equations that remain invariant under Lorentz transformations, essential for describing high-energy phenomena. The relativistic Duffin-Kemmer-Petiau (DKP) equation describes spin-zero and spin-one particles. The study emphasizes the DKP equation's application in one-dimensional systems, particularly under the influence of a Woods-Saxon potential well. The project aims to analytically solve the DKP equation for a Woods-Saxon potential well, demonstrating the presence of pair creation and antiparticle-bound states. The research involves deriving the DKP equation for a generic potential, solving it in both positive and negative regions, and studying the asymptotic behavior of solutions to identify bound states. Energy eigenvalues and turning points for pair creation are also determined. This study supports the equivalence of spin-one and spin-zero using a formalism in (1+1) dimensions and compares it to the process in (3+1) dimensions. This emphasizes the critical values where pair creation dominates and provides solutions for the DKP equation and its associated physical phenomena.

• Κύριος συγγραφέας: Garzón Pardo, Alexis Mauricio (author)
• Μορφή: bachelorThesis
• Γλώσσα: eng
• Έκδοση: 2025
• Θέματα: Mecánica cuántica relativista; Mecanismo de creación de pares; Funciones hipergeométricas; Relativistic quantum mechanics; Pair creation mechanism; Hypergeometric functions
• Διαθέσιμο Online: http://repositorio.yachaytech.edu.ec/handle/123456789/924