Método de iteración asintótica: átomo de hidrógeno, grafeno, modos cuasi normales

Authors

  • M. Jimenez Autonomous University of the State of Hidalgo
  • N. Y. López Autonomous University of the State of Hidalgo
  • O. Pedraza Universidad Autónoma del Estado de Hidalgo
  • L. A. López Universidad Autónoma del Estado de Hidalgo

DOI:

https://doi.org/10.31349/RevMexFis.22.020202

Keywords:

AIM, Hydrogen Atom, Graphene, Quasi--normal modes

Abstract

En este trabajo se muestra como el Método de Iteración Asintótica (AIM por sus siglas en inglés) puede ser empleado para obtener eigenvalores y eigenfuciones en diferentes campos de la física. Partiendo de la ecuación de Schrödinger en cada caso, se pueden calcular la energía y las funciones de onda del Átomo de Hidrógeno o los modos cuasi--normales en el caso de agujeros negros. El objetivo central, es mostrar cómo aplicar el Método de Iteración Asintótica en algunas áreas de la Física.

 

In this work, we show how the Asymptotic Iteration Method (AIM) can be used to obtain eigenvalues and eigenfunctions in different fields of physics. Starting from the Schr\"odinger equation in each case, the energies and wave functions of the Hydrogen Atom or the quasi-normal modes in the case of black holes can be calculated. The central objective is to show how to apply the Asymptotic Iteration Method in some areas of Physics.

References

E. W. Leaver. An analytic representation for the quasinormal modes of kerr black holes. Proc. R. Soc. London. A. Math. Phys. Sci. 402 (1985) 285. https://doi.org/10.1098/rspa.1985.0119

M. Eshghi and H. Mehraban. Exact solution of the diracweyl equation in graphene under electric and magnetic fields. Comptes Rendus Physique, 18 (2017) 47. Prizes of the French Academy of Sciences 2015 Prix de l’Académie des sciences 2015. https://doi.org/10.1016/j.crhy. 2016.06.002

R. Arceo, L. M. Sandoval, O. Pedraza, L. A. López, G. León-Soto, and J. Martínez-Castro. Elastic scattering for π + p using the Klein-Gordon equation. Int. J. Mod. Phys. E, 30 (2021) 2150048. https://doi.org/10.1142/S0218301321500488

E. Hairer, C. Lubich, and M. Roche. The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods. Lecture Notes in Mathematics. (Springer Berlin Heidelberg, 2006). https://doi.org/10.1007/BFb0093947

H. Ciftci, R. L. Hall, and N. Saad. Asymptotic iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 36 (2003) 11807. https://dx.doi.org/10.1088/0305-4470/36/47/008

O. Bayrak and I. Boztosun. Application of the asymptotic iteration method to the exponential cosine screened coulomb potential. Int. J. Quantum Chem., 107 (2007) 1040. https://doi.org/10.1002/qua.21240

M. Karakoc¸, Aimpy: A python code to solve Schrödinger-like equations with the asymptotic iteration method. Int. J. Mod. Phy. C, 32 (2021) 2150017. https://doi.org/10.1142/S0129183121500170

N. Y. López-Juárez, O. Pedraza-Ortega, L. A. López- Suárez, and R. Arceo-Reyes. Estados ligados en el grafeno en presencia de campo magnético. Pädi Boletín Científico de Ciencias Básicas e Ingenierías del ICBI, 11 (2023) 161. https://doi.org/10.29057/icbi.v11iEspecial5.11716

K. S. Alsadi. Bound state solutions of a dirac particle undergoing a tensor interaction potentials via asymptotic iteration method. J. Taibah Univ. Sci., 14 (2020) 1156. https://doi.org/10.1080/16583655.2020.1807129

M. Jiménez-Camargo, O. Pedraza-Ortega, and L. A. López-Suárez. Modos cuasi normales para un agujero negro schwarzschild de sitter rodeado de quintaesencia: Método de iteración asintótica. Pädi Boletín Científico de Ciencias Básicas e Ingenierías del ICBI, 10 (2022) 29. https://doi.org/10.29057/icbi.v10iEspecial.8244

H. T. Cho et al., A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method, Adv. Math. Phys. 2012 (2012) 281705, https://doi.org/10.1155/2012/281705

I. Boztosun, M. Karakoc, F. Yasuk, and A. Durmus. Asymptotic iteration method solutions to the relativistic Duffin-KemmerPetiau equation. J. Math. Phys. 47 (2006) 062301. https://doi.org/10.1063/1.2203429

H. Ciftci, R. L. Hall, and N. Saad. Perturbation theory in a framework of iteration methods. Phys. Lett. A, 340 (2005) 388. https://doi.org/10.1016/j.physleta.2005.04.030

S. Kuru, J. Negro, and L. M. Nieto. Exact analytic solutions for a dirac electron moving in graphene under magnetic fields. J. Phys.: Condens. Matter., 21 (2009) 455305. https://dx.doi.org/10.1088/0953-8984/21/45/455305

R. A. Konoplya and Alexander Zhidenko. Quasinormal modes of black holes: From astrophysics to string theory. Rev. Mod. Phys., 83 (2011). 793 https://doi.org/10.1103/RevModPhys.83.793

E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Class. Quantum Grav. 26 (2009) 163001, https://dx.doi.org/10.1088/0264-9381/26/16/163001

V.V. Kiselev. Quintessence and black holes. Class. Quant. Grav. 20 (2003) 1187. https://dx.doi.org/10.1088/0264-9381/20/6/310

G. Barrientos, O. Pedraza, L. A. López, and R. Arceo. Modos cuasi-normales de un agujero negro de Einstein-Gaussbonnet rodeado de quintaesencia: perturbaciones escalares y electromagnéticas. Rev. Mex. Fis., 68 (2022) 050704. https://doi.org/10.31349/RevMexFis.68.050704

Downloads

Published

2025-07-01

How to Cite

[1]
M. Jimenez, N. Y. L´ópez, omar pedraza, and L. A. L´opez, “Método de iteración asintótica: átomo de hidrógeno, grafeno, modos cuasi normales”, Rev. Mex. Fis. E, vol. 22, no. 2 Jul-Dec, pp. 020202 1–, Jul. 2025.

Issue

Vol. 22 No. 2 Jul-Dec (2025): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2025 M. Jimenez, N. Y. López, O. Pedraza, L. A. López

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.