{"paper":{"title":"A Statistical Interpretation of Space and Classical-Quantum duality","license":"","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Alon E. Faraggi, Marco Matone","submitted_at":"1996-06-12T05:04:03Z","abstract_excerpt":"By defining a prepotential function for the stationary Schr\\\"odinger equation we derive an inversion formula for the space variable $x$ as a function of the wave-function $\\psi$. The resulting equation is a Legendre transform that relates $x$, the prepotential ${\\cal F}$, and the probability density. We invert the Schr\\\"odinger equation to a third-order differential equation for ${\\cal F}$ and observe that the inversion procedure implies a $x$-$\\psi$ duality. This phenomenon is related to a modular symmetry due to the superposition of the solutions of the Schr\\\"odinger equation. We propose tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9606063","kind":"arxiv","version":3},"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"}