Interpretation of the q-Deformed 1-D Quantum Harmonic Oscillator
Bibliographic record
Abstract
The interpretation of the q-deformed 1-D quantum harmonic oscillator is investigated for two definitions of q-deformation. This investigation is achieved by using Zaslavskii's method to obtain the Heisenberg equations of motion (quantum Liouville equations) in the undeformed phase space. These quantum Liouville equations exhibit a non-commutative geometry produce from the existence of the dilatation operator which is inherent in the q-deformation process. The classical limits of these equations are obtained by applying a special classical limiting condition to produce the classical Liouville equations of the q-deformed oscillator. These classical Liouville equations are solved by using the method of characteristics in order to obtain the classical probability distribution functions for this system. The 2-D and 3-D behaviors of these functions were then investigated using a computer visualization method. The results of the mathematical derivations together with the computer visualization method show that the classical limit of the quantum Liouville equations for the q-deformed 1-D quantum harmonic oscillator are statistical in nature where the nonlinearity parameter for the q-deformed oscillator is connected with h . This result conforms to that obtained by Ghosh et al. for the undeformed 1-D quantum harmonic oscillator.
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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 | 0.001 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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".