Double exponential Sinc numerical methods for the two-dimensional time-independent Schrödinger equation
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Bibliographic record
Abstract
In this work, the Sinc collocation and Sinc–Galerkin methods are applied in conjunction with double exponential transformations to solve the two-dimensional time-independent Schrödinger equation. The block centrosymmetry is introduced as a two-dimensional extension of the well-known centrosymmetric property. It helps to significantly reduce the computational time while calculating the eigenvalues of the system matrices. Numerical examples with a variety of separable and nonseparable potential functions are presented. A comparison between the single and double exponential Sinc methods confirms the efficiency and superiority of the double exponential Sinc methods.
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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 | 0.001 | 0.001 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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