WKB approach to calculating the lifetime of quasistationary states: Harmonic oscillator in a polynomial perturbation
Bibliographic record
Abstract
A simple and straightforward WKB approach to calculating the lifetime of quasistationary states in spherically symmetric potential wells is suggested. Using this approach, a general formula for the imaginary part of the energy for potentials of the form $V(x)=P(x)\ensuremath{-}\ensuremath{\mu}Q(x)\mathrm{---}\mathrm{where}$ $P(x)$ is the radial part of the potential for a spherically symmetric harmonic oscillator and $Q(x)$ is an even polynomial---is derived. Using this formula, the usual tedious procedure of the explicit asymptotic matching of the WKB and perturbative wave functions is avoided, and calculations are substantially simplified. The leading term and a few corrections of the series for the imaginary part of the energy and the related lifetime are analytically calculated.
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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".