Coherent states sometimes look like squeezed states and vice versa: the Paul trap
Bibliographic record
Abstract
Abstract. Using the Paul Trap as a model, we point out that the same wave functions can be variously coherent or squeezed states, depending upon the system they are applied to. 1 Coherent/squeezed states and their uncertainty relations Elsewhere [1, 2], we have investigated Schrödinger Equations that are quadratic in x and p operators with time-dependent coefficients. The Hamiltonians are parts of general Lie space-time symmetry algebras that are products of a Heisenberg-Weyl algebra with an su(1, 1) algebra: i.e., the algebras associated with the harmonic-oscillator coherent states and their squeezing. Concentrating first on coherent states, the (time-dependent) lowering and raising (ladder) operators are given by A(t) = i [gp(t) p − gx(t) x + gI(t)] , A † (t) = −i [ g ∗ p (t) p − g ∗ x (t) x + g ∗ I (t)] , (1) 1
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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 | 0.001 |
| 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".