Analytical energy eigenvalues of a Dirac particle in focusing field of a quadrupole magnet
Bibliographic record
Abstract
In this study, the motion of a charged spin-1/2 fermion is found out. It is assumed, in the system, that the free fermion is subjected to a linearly space-dependent magnetic field that can be supposed to be a focusing magnetic field of a quadrupole magnet in beam dynamics in the accelerator physics. In such an examination, two-component Dirac equation is solved via perturbation approximation of the asymptotic iteration method (AIM), which has been widely used for the last decades. The results show that the fermion is bounded to the magnetic field for a certain condition of the strength of the field. For such a system, the analytical form of the energy eigenvalues are obtained. Moreover, to see whether this analytical expression works properly, the numerical eigenvalues are compared with the ones obtained by direct use of the AIM. We have an inspiration that the studies on beam dynamics and magnet design in particle accelerator physics may gain from this work.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".