Compression effects on dipole transitions and state lifetimes for a hydrogen atom
Bibliographic record
Abstract
The quantum mechanical problem of a hydrogen atom placed at the center of an impenetrable sphere of radius r 0 is solved by using two different methods, where, in the first, a trial wave function, consisting of a hydrogen-like function times a cutoff factor that ensures fulfillment of Dirichlet boundary condition, is proposed, whereas in the second, the radial Schrödinger equation is solved by means of an accurate numerical technique. We computed the energies for the ground and first excited states of S-, P-, and D-symmetry, as well as dipole transitions, oscillator strengths, and a few state lifetimes. Although the variational method and the numerical solution are found to give similar qualitative behaviours, which, in general, compare reasonably well with some results published previously, the 2p state lifetimes obtained in the present calculations appear to be at variance with the latter at some particular box radii.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".