dorsal/arxiv
View SchemaTwo-Body Interaction. I. Inverse Scattering Problem, Nonlocal Potentials, and a Conception of Quantum Measurement Theory
| Authors | V. M. Muzafarov |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0702053 |
| URL | https://arxiv.org/abs/nucl-th/0702053 |
| DOI | 10.1134/S1061920807010062 |
| Journal | Russian J. Math Phys. 14:1 (2007) 96-109 |
Abstract
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a nontraditional setting: the scattering wave function in the momentum representation is recovered immediately from the scattering data. The solution we find for the problem in question is given by a family of phase-equivalent wave functions with explicitly controlled functional-analytic arbitrariness. This arbitrariness corresponds to the arbitrariness in the choice of phase-equivalent nonlocal potentials and causes the necessary to include some additional concepts of quantum measurement theory to a complete description of quantum-mechanical systems. The mathematical apparatus of the approach thus developed is illustrated by the example of describing the nucleon-nucleon interaction in uncoupled partial channels.
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"abstract": "The present paper generalizes preceding papers of the author and opens a\ncycle of works concerning the general posing and solution in analytic form of\nthe quantum-mechanical inverse scattering problem (for a given partial channel)\nin a nontraditional setting: the scattering wave function in the momentum\nrepresentation is recovered immediately from the scattering data. The solution\nwe find for the problem in question is given by a family of phase-equivalent\nwave functions with explicitly controlled functional-analytic arbitrariness.\nThis arbitrariness corresponds to the arbitrariness in the choice of\nphase-equivalent nonlocal potentials and causes the necessary to include some\nadditional concepts of quantum measurement theory to a complete description of\nquantum-mechanical systems. The mathematical apparatus of the approach thus\ndeveloped is illustrated by the example of describing the nucleon-nucleon\ninteraction in uncoupled partial channels.",
"arxiv_id": "nucl-th/0702053",
"authors": [
"V. M. Muzafarov"
],
"categories": [
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"doi": "10.1134/S1061920807010062",
"journal_ref": "Russian J. Math Phys. 14:1 (2007) 96-109",
"title": "Two-Body Interaction. I. Inverse Scattering Problem, Nonlocal Potentials, and a Conception of Quantum Measurement Theory",
"url": "https://arxiv.org/abs/nucl-th/0702053"
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