Quantum Mechanical Numerical Study of Low-Energy States and Tunneling in 1D Tunable Multi-Gaussian Potentials
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2025
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| _version_ | 1866902165796159488 |
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| author | Ahmos, Ivan |
| author_facet | Ahmos, Ivan |
| contents | <p>This study presents a numerical investigation of a one-dimensional quantum mechanical system using finite-difference methods. The work focuses on solving the time-independent Schrödinger equation for a custom-defined potential, exploring the dependence of eigenvalues on system parameters such as λ and the domain length L. The computational approach was implemented in Python, with the model reformulated into a matrix eigenvalue problem after de-dimensionalization. Results include analyses of how λ affects the shape of the eigenfunctions and the energy level spacing ΔE as a function of L. This paper demonstrates the effectiveness of numerical methods in visualizing and interpreting bound-state solutions in nontrivial potentials, supported by pseudocode and graphical results.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17509040 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quantum Mechanical Numerical Study of Low-Energy States and Tunneling in 1D Tunable Multi-Gaussian Potentials Ahmos, Ivan Quantum physics <p>This study presents a numerical investigation of a one-dimensional quantum mechanical system using finite-difference methods. The work focuses on solving the time-independent Schrödinger equation for a custom-defined potential, exploring the dependence of eigenvalues on system parameters such as λ and the domain length L. The computational approach was implemented in Python, with the model reformulated into a matrix eigenvalue problem after de-dimensionalization. Results include analyses of how λ affects the shape of the eigenfunctions and the energy level spacing ΔE as a function of L. This paper demonstrates the effectiveness of numerical methods in visualizing and interpreting bound-state solutions in nontrivial potentials, supported by pseudocode and graphical results.</p> |
| title | Quantum Mechanical Numerical Study of Low-Energy States and Tunneling in 1D Tunable Multi-Gaussian Potentials |
| topic | Quantum physics |
| url | https://doi.org/10.5281/zenodo.17509040 |