Bibliographic record
Abstract
The harmonic oscillator represents as a unique tool in modern physics since it is not only exactly solvable but also relates many phenomena. This paper introduces the relation between Quantum Field Theory and other physical theories and discusses how harmonic oscillator behave in Quantum Mechanics and Quantum Field Theory by the quantization of Klein-Gordon Field. To this end, this paper applies energy-momentum equation given by special relativity to Schrödinger’s Equation to get the Klein-Gordon Field, and then uses canonical method to quantize the field, which is called the second quantization of the field. The comparison is made between the result quantized field, the quantum harmonic oscillator and classical harmonic oscillator. The similarity of two physical systems is demonstrate by the comparison between commutation relations of operators. The similar commutation relations then help people to interpret quantized Klein-Gordon Field as a system that contain a quantized harmonic oscillator in each space coordinate.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.004 | 0.014 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.004 | 0.012 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".