{"paper":{"title":"Hermitian Hamiltonians: Matrix versus Schr${\\\"o}$dinger's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Achint Kumar, Ankush Singhal, Mohammad Irfan, Zafar Ahmed","submitted_at":"2016-07-13T13:16:27Z","abstract_excerpt":"We draw attention to the fact that a Hermitian matrix is always diagonalizable and has real discrete spectrum whereas the Hermitian Schr{\\\"o}dinger Hamiltonian: $H=p^2/2\\mu+V(x)$, may not be so. For instance when $V(x)=x, x^3, -x^2$, $H$ does not have even one real discrete eigenvalue. Textbooks do not highlight this distinction. However, if $H$ has real discrete spectrum, by virtue of the expansion theorem, one can convert the eigenvalue problem $H\\psi_n=E_n \\psi_n$ into a matrix and get eigenvalues $E_n$ by diagonalizing the matrix. We show, that the thus obtained $E_n$ could be accurate, pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01543","kind":"arxiv","version":2},"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"}