Corrected non-relativistic bound state solutions in <i>D</i>-dimensional Euclidean space for the Hua potential
Bibliographic record
Abstract
In this work, we present a rigorous and complete non-relativistic treatment of the problem of a diatomic molecule which moves under the Hua potential in a D-dimensional Euclidean space. The radial Green’s function associated with this potential is constructed within the framework of the Feynman path integral. Different cases of this potential which are distinguished by the values of the deformation parameter q are considered separately. For [Formula: see text] q < 1 and r ∈ ] r0, +∞[, we adopt an appropriate Pekeris-type approximation for the centrifugal potential term to obtain the approximate spectrum of bound states lD ≠ 0. Some numerical results of the energy levels of certain diatomic molecules are calculated by using the correct minimum value of the deformation parameter q given by [Formula: see text]. For q < 0 or [Formula: see text], the problem is solvable only in a three-dimensional space. In both cases, the energy quantization condition is a transcendental equation that can be solved numerically. In the limit [Formula: see text], the energy spectrum and the corresponding wave functions of the radial Morse potential are regained.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".