Resonant-State Expansion Applied to Non-Relativistic Wave Equation in One-Dimension

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Published: Nov 10, 2024
DOI: https://doi.org/10.56919/usci.2434.021
Keywords:
Resonant-states expansion, unperturbed basis, non-relativistic wave equation, perturbation theory

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Abdullahi Tanimu
Department of Physics, Faculty of Natural and Applied Science, Umaru Musa Yar'adua University, P. M. B. 2218, Katsina State, Nigeria
https://orcid.org/0000-0002-0550-2726
Ibrahim Muhammad Bagudo
Department of Physics, Faculty of Natural and Applied Science, Umaru Musa Yar'adua University, P. M. B. 2218, Katsina State, Nigeria
https://orcid.org/0000-0001-8004-801X
Haruna Abdullahi Abubakar
Energy Commission of Nigeria, CBD, Abuja

Abstract

Study’s Excerpt



  • The rigorous resonant-state expansion (RSE) method is extended to the non-relativistic one-dimensional wave equation.

  • Resonant states (RSs) wave numbers as the unperturbed basis were employed to confirm the RSE's convergence to exact solutions.

  • RSE's has potentials for systematically calculating RSs in complex quantum systems with multi-well potentials.


Full Abstract


The resonant-state expansion (RSE), a rigorous perturbation theory recently developed in electrodynamics, is here applied to the non-relativistic wave equation in one-dimension. The resonant states (RSs) wave numbers for the double well system are analytically calculated and used as the unperturbed basis for calculating the RSE. We demonstrate the efficiency of the RSE by verifying its convergence to the exact solution for a triple well potential. We show that for the chosen perturbations (i.e., for and ), the method is particularly suitable for calculating all the RSs within the spectrum.

Article Details

How to Cite
Tanimu, A., Bagudo, I. M., & Abubakar, H. A. (2024). Resonant-State Expansion Applied to Non-Relativistic Wave Equation in One-Dimension. UMYU Scientifica, 3(4), 275–280. https://doi.org/10.56919/usci.2434.021
Issue
Vol. 3 No. 4 (2024): UMYU Scientifica, Volume 3, Issue 4, December 2024
Section
Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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