Inverse problem in energy-dependent potentials using semiclassical methods
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929374223138816 |
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| author | Albuquerque, Saulo Völkel, Sebastian H. Kokkotas, Kostas D. |
| author_facet | Albuquerque, Saulo Völkel, Sebastian H. Kokkotas, Kostas D. |
| contents | Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound states of potential wells and reflection/transmission coefficients in terms of the Bohr-Sommerfeld rule and the Gamow formula. We then discuss the inverse problem, in which the latter observables are used as a starting point to reconstruct the properties of the potentials. By extending known inversion techniques to energy-dependent potentials, we demonstrate that so-called width-equivalent or WKB-equivalent potentials are not isospectral anymore. Instead, we explicitly demonstrate that constructing quasi-isospectral potentials with the inverse techniques is still possible. Those reconstructed, energy-independent potentials share key properties with the width-equivalent potentials. We report that including energy-dependent terms allows for a rich phenomenology, particularly for the energy-independent equivalent potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse problem in energy-dependent potentials using semiclassical methods Albuquerque, Saulo Völkel, Sebastian H. Kokkotas, Kostas D. High Energy Physics - Phenomenology General Relativity and Quantum Cosmology Quantum Physics Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound states of potential wells and reflection/transmission coefficients in terms of the Bohr-Sommerfeld rule and the Gamow formula. We then discuss the inverse problem, in which the latter observables are used as a starting point to reconstruct the properties of the potentials. By extending known inversion techniques to energy-dependent potentials, we demonstrate that so-called width-equivalent or WKB-equivalent potentials are not isospectral anymore. Instead, we explicitly demonstrate that constructing quasi-isospectral potentials with the inverse techniques is still possible. Those reconstructed, energy-independent potentials share key properties with the width-equivalent potentials. We report that including energy-dependent terms allows for a rich phenomenology, particularly for the energy-independent equivalent potentials. |
| title | Inverse problem in energy-dependent potentials using semiclassical methods |
| topic | High Energy Physics - Phenomenology General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2404.11478 |