Double well potentials with a quantum moat barrier or a quantum wall barrier give rise to similar entangled wave functions
Bibliographic record
Abstract
The solution to a problem in quantum mechanics is generally a linear superposition of states. The solutions for double well potentials epitomize this property, and go even further than this: they can often be described by an effective model whose low energy features can be described by two states—one in which the particle is on one side of the barrier, and a second where the particle is on the other side. Then the ground state remains a linear superposition of these two macroscopic-like states. In this paper, we illustrate that this property is achieved similarly with an attractive potential that separates two regions of space, as opposed to the traditionally repulsive one. In explaining how this comes about we revisit the concept of “orthogonalized plane waves,” first discussed in 1940 to understand electronic band structure in solids, along with the accompanying concept of a pseudopotential. We show how these ideas manifest themselves in a simple double well potential, whose “barrier” consists of a moat instead of the conventional wall.
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 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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.001 | 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 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".