Parabolic band approximation of the electron energy levels in a tetrahedral-shaped quantum dot
Bibliographic record
Abstract
In more elaborate schemes, an electron’s effective mass in a heterostructure semiconductor quantum dot (QD) depends on both its position and its energy. However, the electron’s effective mass can be simply modeled by a parabolic band approximation — the electron’s effective mass inside the QD — which is assumed to be constant and differs from the one outside the QD, which is also assumed to be constant. The governing equation to be solved for the electron’s energy levels inside the QD is the nonlinear Schrödinger equation. With the approximation, the nonlinear Schrödinger equation for a tetrahedral-shaped QD is discretized by using the finite-volume method. The discretized nonlinear Schrödinger equation is solved for the electron energy levels by a computer program. It is noted that the resulting energy levels for the parabolic mass model are nondegenerate due to the mass-gradient term at the corners, edges, and surfaces of the tetrahedral-shaped QD.PACS Nos.: 02.60.Cb, 03.65.Ge, 81.07.Ta
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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".