Resonant-State Expansion Applied to Non-Relativistic Wave Equation in One-Dimension
DOI:
https://doi.org/10.56919/usci.2434.021Keywords:
Resonant-states expansion, unperturbed basis, non-relativistic wave equation, perturbation theoryAbstract
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.
References
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Copyright (c) 2024 Abdullahi Tanimu, Ibrahim Muhammad Bagudo, Haruna Abdullahi Abubakar
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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