{"paper":{"title":"New exact solutions of the 3D Schr\\\"odinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A.S. Medvedev, B.I. Sadovnikov, E.E. Perepelkin, N.G. Inozemtseva","submitted_at":"2025-06-05T08:01:44Z","abstract_excerpt":"Previously we found a unique quantum system with a positive gauge-invariant Weyl-Stratonovich quasi-probability density function which can be defined by the so-called {\\guillemotleft}quadratic funnel{\\guillemotright} potential [Phys. Rev. A 110 02222 (2024)]. In this work we have constructed a class of exact solutions to the 3D Schr\\\"odinger equation for a two-parameter {\\guillemotleft}quadratic funnel{\\guillemotright} potential based on the -model of micro and macro systems. Explicit expressions for the energy spectrum and the set of eigenfunctions have been found. Using gauge invariance for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04725","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04725/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}