Transmission and reflection of a molecule with a dipole moment incident upon a circular hole in a two-dimensional conducting sheet
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Bibliographic record
Abstract
Abstract We consider a one-dimensional molecule with a permanent electric dipole moment incident along the line of symmetry of a circular hole in an infinite two-dimensional conducting sheet. We calculate the probabilities of reflection p R and transmission p T of a centre of mass wave packet initially of the form of a Gaussian wave packet and moving toward the hole. We show the dependence of p T and p R on the charge Q of the atoms, the radius a of the hole as compared to the length scale <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>α</mml:mi> </mml:math> of the bound molecular relative motion state, the mass and energy of the molecule. We compare a fully quantum mechanical treatment to a semiclassical approximation in which the distance between the atoms is constant. Some unexpected and surprising results emerge from this study.
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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 it