{"paper":{"title":"New Exactly and Conditionally Exactly Solvable N-Body Problems in One Dimension","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"C. Nagaraja Kumar, N. Gurappa, Prasanta. K. Panigrahi","submitted_at":"1996-04-19T05:05:40Z","abstract_excerpt":"We study a class of Calogero-Sutherland type one dimensional N-body quantum mechanical systems, with potentials given by $$ V( x_1, x_2, \\cdots x_N) = \\sum_{i <j} {g \\over {(x_i - x_j)^2}} - \\frac{g^{\\prime}}{\\sum_{i<j}(x_i - x_j)^2} + U(\\sqrt{\\sum_{i<j}(x_i - x_j)^2}),$$ where $U(\\sqrt{\\sum_{i<j}(x_i - x_j)^2})$'s are of specific form. It is shown that, only for a few choices of $U$, the eigenvalue problems can be solved {\\it exactly}, for arbitrary $g^{\\prime}$. The eigen spectra of these Hamiltonians, when $g^{\\prime} \\ne 0$, are non-degenerate and the scattering phase shifts are found to b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9604109","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}