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Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schr\\\"odinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2.\n  It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. Given a kernel K_1 o"},"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":"1111.4449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-18T18:20:06Z","cross_cats_sorted":["math.CA","math.MP","quant-ph"],"title_canon_sha256":"b89295fc8efcb5e3a4d9007bde53e54fdbfb731ec1810366fcfb586fd9b561ec","abstract_canon_sha256":"50dff504595c361879be095013045508cbe5b4141c5a45196f83789d123dbd8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:47.522554Z","signature_b64":"huWb60gyvqDsv+KnrYULmoJ3TJdDOu9BaF7R3lJ5PYln0VGFgcZlm8rzARA66br1T0SwgGsh3XNGgjnPLvTQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9a3d9461c8df1f59da06711ba904039396908271d580971df6ef67937ed1fd3","last_reissued_at":"2026-05-18T03:46:47.521824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:47.521824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transmutations for Darboux transformed operators with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Sergii M. Torba, Vladislav V. Kravchenko","submitted_at":"2011-11-18T18:20:06Z","abstract_excerpt":"We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schr\\\"odinger operator. Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schr\\\"odinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2.\n  It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. 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