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The Hamiltonian $H_L$ converges to $H = -d^2/dx^2 + V_1(x)$ as $L\\to \\infty$ in the strong resolvent sense (and even in the norm resolvent sense for our second case). However, most of the resonances of $H_L$ do not converge to those of $H$. Instead, they crowd together and con"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.03172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-09T08:10:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e103f7dda950c370c8c0663d1bab41edd5d1deaed8b6f12e10703243b2701e89","abstract_canon_sha256":"f0d1d856c8751bcb95aabbb9cc57a89c58681b224bd7ca62409f340d4488f826"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:21.200192Z","signature_b64":"9d13n/V9/jOcy+qboCy6sEbddNRFzZiC+cMqUz7pwvnQQ+CeTUsdPWyW/dZn2f/gkeDl87/ly7WPSg+uLOB5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5217680ce71e35c5c0c7e64258f7dfc63f7f36e96f6162c13bc191d992bd54d5","last_reissued_at":"2026-05-18T00:33:21.199533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:21.199533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resonances - lost and found","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ira Herbst, Richard Froese","submitted_at":"2017-03-09T08:10:32Z","abstract_excerpt":"We consider the large $L$ limit of one dimensional Schr\\\"odinger operators $H_L=-d^2/dx^2 + V_1(x) + V_{2,L}(x)$ in two cases: when $V_{2,L}(x)=V_2(x-L)$ and when $V_{2,L}(x)=e^{-cL}\\delta(x-L)$. This is motivated by some recent work of Herbst and Mavi where $V_{2,L}$ is replaced by a Dirichlet boundary condition at $L$. The Hamiltonian $H_L$ converges to $H = -d^2/dx^2 + V_1(x)$ as $L\\to \\infty$ in the strong resolvent sense (and even in the norm resolvent sense for our second case). However, most of the resonances of $H_L$ do not converge to those of $H$. 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