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Contributions by Heisenberg, Born, Jordan, Dirac and others require separate entries; quantum theory is not credited to one person.", "area": "Quantum mechanics", "topic": "Physics", "year": 1926, "lane": "HUMAN", "result": "THEORY", "package_id": "schrodinger", "target": { "record_id": "urn:uuid:b9ccbf3d-db71-4941-abc2-d7f7eefc164b", "version": 1, "content_hash": "sha256:1804dd2c37e5c057dc95d2a183c875c7cfda3081f0935432dd0ed8fa24fde72c" }, "humans": [ "Erwin Schrödinger" ], "authors_complete": true, "human_role_note": "Listed source contributors; individual labor shares are not measured", "agents": [], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "schrodinger-source", "title": "Schrödinger, Quantisierung als Eigenwertproblem (1926)", "url": "https://doi.org/10.1002/andp.19263840404" } ], "geography": { "country_codes": [ "CH" ], "location_basis": "Documented research locations or paper affiliations for this contribution. 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Contributions by Heisenberg, Born, Jordan, Dirac and others require separate entries; quantum theory is not credited to one person.", "domain": "量子力学" }, "sources": [ { "citation": "Schrödinger, Quantisierung als Eigenwertproblem (1926)", "url": "https://doi.org/10.1002/andp.19263840404" } ], "statement": "# Schrödinger: quantization as an eigenvalue problem\n\n## Why can some systems choose only certain notes?\n\nA guitar string fixed at both ends cannot sustain every possible standing-wave shape. The ends must stay still, which restricts the patterns that fit between them. This familiar picture offers an entry into quantization: a mathematical problem can admit only certain allowed values. It is an analogy for reading wave mechanics, not a claim that an electron is literally a vibrating piece of string.\n\n## What an eigenvalue means\n\nAn operator is a rule that acts on a function. For certain special functions, applying that rule changes only the overall multiplier, not the function’s shape. The function is an eigenfunction and the multiplier is an eigenvalue. In a stationary quantum problem, the relevant operator represents energy. The equation asks which wavefunctions have a definite energy while also satisfying the physical conditions of that particular problem.\n\n## Try an invented boundary-condition example\n\nDraw a length of string and sketch a standing wave that is zero at each end. One half-wave fits. Two half-waves fit too, while one and a half generally leaves the final end away from zero. With the same string length, the first two patterns have wavelengths twice the length and equal to the length. Boundary conditions have selected a list. The example explains selection; it does not calculate an atomic energy.\n\n## What changed in the recorded work\n\nSchrödinger’s 1926 work made quantization an eigenvalue problem in wave mechanics. That supplied a systematic mathematical way to pose and solve quantum questions. This entry does not transfer the work of Heisenberg, Born, Jordan, Dirac or others to one author. The equation’s usefulness also depends on choosing the appropriate physical model: a successful solution of a simplified equation does not automatically include every interaction in a real atom.\n\n## A manageable next step\n\nAsk your agent to explain one elementary standing-wave problem with its interval, boundary conditions and allowed patterns written next to the answer. Check why a proposed pattern is accepted or rejected. Then identify which parts of the example are only an analogy when discussing quantum wavefunctions. A clear account of these distinctions is a useful contribution without pretending to reconstruct all of quantum mechanics in a short exercise.\n\n## Scientific scope\n\nThis entry records the original wave-mechanics work. Contributions by Heisenberg, Born, Jordan, Dirac and others require separate entries; quantum theory is not credited to one person.\n\n## Sources for this explanation\n\n- [Schrödinger, Quantisierung als Eigenwertproblem (1926)](https://doi.org/10.1002/andp.19263840404): Source for the recorded historical contribution and its scope. Classroom examples below use modern notation and invented values; they are not measurements or quotations from this source.\n", "summary": "Describes quantization through eigenvalue problems in wave mechanics.", "title": "Schrödinger: quantization as an eigenvalue problem" }, "record_id": "urn:uuid:b9ccbf3d-db71-4941-abc2-d7f7eefc164b", "version": 1, "source_ref": { "record_id": "urn:uuid:b9ccbf3d-db71-4941-abc2-d7f7eefc164b", "version": 1, "content_hash": "sha256:1804dd2c37e5c057dc95d2a183c875c7cfda3081f0935432dd0ed8fa24fde72c" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:ebe3ef486463834b570a93a8537f00e7dbc53cbf3dfda9e8d08b7afbe8e73d60" }, "target": { "record_id": "urn:uuid:b9ccbf3d-db71-4941-abc2-d7f7eefc164b", "version": 1, "content_hash": "sha256:1804dd2c37e5c057dc95d2a183c875c7cfda3081f0935432dd0ed8fa24fde72c" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "schrodinger", "entry_id": "schrodinger", "revision": 2, "title": "Schrödinger: quantization as an eigenvalue problem", "context": "Quantum mechanics", "track": "Scoped historical scientific contribution", "band": "S", "modifier": "+", "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-09-14", "evidence_cutoff": "2026-09-14", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Describes quantization through eigenvalue problems in wave mechanics.", "scope": "Wave mechanics and the eigenvalue formulation in the cited 1926 work.", "evidence_summary": "Original sources and institutional historical accounts support the stated contribution. The reading boundary is recorded at each source; this assessment is not an independent scientific verification.", "references": [ { "title": "Schrödinger, Quantisierung als Eigenwertproblem (1926)", "url": "https://doi.org/10.1002/andp.19263840404", "locator": "Retained catalogue source review: Bibliography and stated result; no full proof audit" } ], "roles": [ { "who": "Erwin Schrödinger", "credit": "SCIENCE", "did": "Named source contributor to this scoped work; individual labor shares are not measured." } ], "target": { "record_id": "urn:uuid:b9ccbf3d-db71-4941-abc2-d7f7eefc164b", "version": 1, "content_hash": "sha256:1804dd2c37e5c057dc95d2a183c875c7cfda3081f0935432dd0ed8fa24fde72c" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "700000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "schrodinger", "target": { "record_id": "urn:uuid:b9ccbf3d-db71-4941-abc2-d7f7eefc164b", "version": 1, "content_hash": "sha256:1804dd2c37e5c057dc95d2a183c875c7cfda3081f0935432dd0ed8fa24fde72c" }, "sections": [ { "title": "Why can some systems choose only certain notes?", "text": "A guitar string fixed at both ends cannot sustain every possible standing-wave shape. The ends must stay still, which restricts the patterns that fit between them. This familiar picture offers an entry into quantization: a mathematical problem can admit only certain allowed values. It is an analogy for reading wave mechanics, not a claim that an electron is literally a vibrating piece of string." }, { "title": "What an eigenvalue means", "text": "An operator is a rule that acts on a function. For certain special functions, applying that rule changes only the overall multiplier, not the function’s shape. The function is an eigenfunction and the multiplier is an eigenvalue. In a stationary quantum problem, the relevant operator represents energy. The equation asks which wavefunctions have a definite energy while also satisfying the physical conditions of that particular problem." }, { "title": "Try an invented boundary-condition example", "text": "Draw a length of string and sketch a standing wave that is zero at each end. One half-wave fits. Two half-waves fit too, while one and a half generally leaves the final end away from zero. With the same string length, the first two patterns have wavelengths twice the length and equal to the length. Boundary conditions have selected a list. The example explains selection; it does not calculate an atomic energy." }, { "title": "What changed in the recorded work", "text": "Schrödinger’s 1926 work made quantization an eigenvalue problem in wave mechanics. That supplied a systematic mathematical way to pose and solve quantum questions. This entry does not transfer the work of Heisenberg, Born, Jordan, Dirac or others to one author. The equation’s usefulness also depends on choosing the appropriate physical model: a successful solution of a simplified equation does not automatically include every interaction in a real atom." }, { "title": "A manageable next step", "text": "Ask your agent to explain one elementary standing-wave problem with its interval, boundary conditions and allowed patterns written next to the answer. Check why a proposed pattern is accepted or rejected. Then identify which parts of the example are only an analogy when discussing quantum wavefunctions. A clear account of these distinctions is a useful contribution without pretending to reconstruct all of quantum mechanics in a short exercise." } ], "references": [ { "title": "Schrödinger, Quantisierung als Eigenwertproblem (1926)", "url": "https://doi.org/10.1002/andp.19263840404", "locator": "Source for the recorded historical contribution and its scope. Classroom examples below use modern notation and invented values; they are not measurements or quotations from this source." } ] }, "reading_status": "EXPLANATORY_GUIDE" }