{"paper":{"title":"On the spectrum of the Schr\\\"odinger Hamiltonian of the one-dimensional conic oscillator perturbed by a point interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"L.M. Nieto, M. Gadella, M.L. Glasser, S. Fassari","submitted_at":"2017-06-15T15:12:30Z","abstract_excerpt":"We decorate the one-dimensional conic oscillator $\\frac{1}{2} \\left[-\\frac{d^{2} }{dx^{2} } + \\left|x \\right| \\right]$ with a point impurity of either $\\delta$-type, or local $\\delta'$-type or even nonlocal $\\delta'$-type. All the three cases are exactly solvable models, which are explicitly solved and analysed, as a first step towards higher dimensional models of physical relevance. We analyse the behaviour of the change in the energy levels when an interaction of the type $-\\lambda\\,\\delta(x)$ or $-\\lambda\\,\\delta(x-x_0)$ is switched on. In the first case, even energy levels (pertaining to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04916","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"}