Unified Wronskian formulation of inverse scattering with supersymmetric quantum mechanics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911122859229184 |
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| author | Bozet, Quentin Sparenberg, Jean-Marc |
| author_facet | Bozet, Quentin Sparenberg, Jean-Marc |
| contents | The Wronskian formulation of supersymmetric quantum mechanics (SUSYQM) confluent transformation pairs is applied to the construction of phase-equivalent potentials with different bound spectra, replacing integral formulas. This allows to unify the two steps of a SUSYQM inversion scheme consisting in (i) the construction of a unique bound-state-less potential, possibly singular, from phase-shift inversion by a chain of non-confluent SUSYQM transformations, and (ii) the phase-equivalent addition of bound states by confluent SUSYQM pairs. Both steps are now combined in a single Wronskian formula, providing an elegant complete solution to the fixedangular-momentum inversion problem. This formalism is applied to the inversion of 3S1 and 1S0 neutron-proton data and its numerical implementation is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Wronskian formulation of inverse scattering with supersymmetric quantum mechanics Bozet, Quentin Sparenberg, Jean-Marc Nuclear Theory The Wronskian formulation of supersymmetric quantum mechanics (SUSYQM) confluent transformation pairs is applied to the construction of phase-equivalent potentials with different bound spectra, replacing integral formulas. This allows to unify the two steps of a SUSYQM inversion scheme consisting in (i) the construction of a unique bound-state-less potential, possibly singular, from phase-shift inversion by a chain of non-confluent SUSYQM transformations, and (ii) the phase-equivalent addition of bound states by confluent SUSYQM pairs. Both steps are now combined in a single Wronskian formula, providing an elegant complete solution to the fixedangular-momentum inversion problem. This formalism is applied to the inversion of 3S1 and 1S0 neutron-proton data and its numerical implementation is discussed. |
| title | Unified Wronskian formulation of inverse scattering with supersymmetric quantum mechanics |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2508.19022 |