The Dynamic and Collision Features of Microscopic Particles Described by the Nonlinear Schrödinger Equation in the Nonlinear Quantum Systems
Bibliographic record
Abstract
The dynamic and collision features of microscopic particles described by nonlinear Schrodinger equation are investigated deeply using the analytic and the Runge-Kutta method of numerical simulation. The results show that the microscopic particles have a wave-corpuscle duality and are stable in propagation. When the two microscopic particles are collided, they can go through each other and retain their form after their collision of head-on from opposite directions, This feature is the same with that of the classical particles. However, a wave peak of large amplitude, which is a result of complicated superposition of two solitary waves, occurs in the colliding process. This displays the wave feature of microscopic particles. Therefore, the collision process shows clearly that the solutions of the nonlinear Schrodinger equation have a both corpuscle and wave feature, then the microscopic particles represented by the solutions have a wave-corpuscle duality. Obviously, this is due to the nonlinear interaction b||2. Thus we can determine the nonlinear Schrodinger equation can describe correctly the natures and properties of microscopic particles in quantum systems. Key words: Microscopic particle Schrodinger equation; Wave-corpuscle duality; Nonlinear interaction; Collision; Propagation; Quantum mechanics
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".