Pith. Sign in

RECORD

Approximating the ground state eigenvalue via the effective potential

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Ilias Chenn, Wei Wang, Shiwen Zhang

Spectral Theory · Submitted 11 Jul 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For the 1-d continuous Anderson Bernoulli model, we show that the ratio of the ground state energy and the minimum of the effective potential approaches $\frac{\pi^2}{8}$ as the domain size approaches infinity.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2107.04969 (version 2)
Pith IDT45ME3BS, Pith's permanent record of this paper and its review
CitationIlias Chenn, Shiwen Zhang, Wei Wang. "Approximating the ground state eigenvalue via the effective potential." arXiv:2107.04969 (2021). https://pith.science/paper/T45ME3BS
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,208 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.02 · states quantitative result 0.98 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper, we study 1-d random Schr\"odinger operators on a finite interval with Dirichlet boundary conditions. We are interested in the approximation of the ground state energy using the minimum of the effective potential. For the 1-d continuous Anderson Bernoulli model, we show that the ratio of the ground state energy and the minimum of the effective potential approaches $\frac{\pi^2}{8}$ as the domain size approaches infinity. Besides, we will discuss various approximations to the ratio in different situations. There will be numerical experiments supporting our main results for the ground state energy and also supporting approximations for the excited states energies.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we study 1-d random Schr\"odinger operators on a finite interval with Dirichlet boundary conditions. background 0.61 0.55 0.02 asserted 0.75
s1 We are interested in the approximation of the ground state energy using the minimum of the effective potential. contribution 0.67 0.32 0.07 unclear 0.61
s2 For the 1-d continuous Anderson Bernoulli model, we show that the ratio of the ground state energy and the minimum of the effective potential approaches $\frac{\pi^2}{8}$ as the domain size approaches infinity. result 1.00 0.95 0.89 asserted 1.00
s3 Besides, we will discuss various approximations to the ratio in different situations. contribution 0.89 0.55 0.03 unclear 0.61
s4 There will be numerical experiments supporting our main results for the ground state energy and also supporting approximations for the excited states energies. method 0.52 0.85 0.04 asserted 0.86

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper, we study 1-d random Schr\"odinger operators on a finite interval with Dirichlet boundary conditions. We are interested in the approximation of the ground state energy using the minimum of the effective potential. For the 1-d continuous Anderson Bernoulli model, we show that the ratio of the ground state energy and the minimum of the effective potential approaches $\frac{\pi^2}{8}$ as the domain size approaches infinity. Besides, we will discuss various approximations to the ratio in different situations. There will be numerical experiments supporting our main results for the ground state energy and also supporting approximations for the excited states energies.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

3 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Cites it as support 1 paper
Cites it as background 1 paper

What it cites

Cites as background 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.