{"paper":{"title":"Canonical Quantization, Quasi-Hermiticity, Observables and the Construction of Complete Basis Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cameron L. Williams, Donald J. Kouri, Nikhil Pandyaq","submitted_at":"2016-10-16T23:03:22Z","abstract_excerpt":"We consider the problem of designing a variety of \"system guided\" basis sets for quantum mechanical anharmonic oscillators. Using ideas based on supersymmetric quantum mechanics, we design canonical transformations of the usual position and momentum to generate generalized \"Cartesian-like positions, W and momenta, p_W\" with unit Poisson brackets. These are quantized following Dirac, leading to an infinite family of potential \"operator observables\". The fundamental issue is that all but one of the operators are not Hermitian (formally self-adjoint) in the original position representation. We sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04925","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"}