Bibliographic record
Abstract
In 1937, Rabi treated the problem of a magnetic moment in an applied time-dependent magnetic field. This became the well-known magnetic resonance situation. The Hamiltonian is often taken to be [Formula: see text] = – µ · [[Formula: see text]]. In this paper, the Rabi oscillations formula, describing the spin flipping, is derived in an unusual way. The method uses a modification of a method due to Heitler. In the Heitler method, one uses the Interaction Picture of quantum mechanics. Due to the time-dependence in the problem, the usual Heitler method fails. However, the solution is found after quantizing the electromagnetic field. To better understand the origin of the spin flipping, the analogous time-independent problem is also solved. It is made clear that the origin of the Rabi oscillations is not due to the time-dependent magnetic field. The spin flipping is essentially due to the fact that the spin system, when initially prepared, is not in an eigenstate of the Hamiltonian. Thus, as times progresses, the system naturally evolves through the noneigenstate basis states.PACS Nos.: 03.65.–w, 76.20.+q
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".