Bibliographic record
Abstract
Abstract A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates nonuniform and optimal spatial discretization. Applications have been made to calculate the energies, densities, and expectation values for two singular potentials of physical interest, viz., (i) the harmonic potential plus inverse quartic and sextic perturbation and (ii) the Coulomb potential with a linear and quadratic term for a broad range of parameters. The first 10 states belonging to a maximum of 𝓁 = 8 and 5 for (i) and (ii) have been computed with good accuracy and compared with the most accurate available literature data. The calculated results are in excellent agreement, especially in light of the difficulties encountered in these potentials. Some new states are reported here for the first time. This offers a general and efficient scheme for calculating these and other similar potentials of physical and mathematical interest in quantum mechanics accurately. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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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 | 0.001 | 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".