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Coherent States for Transparent Potentials

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Boris F. Samsonov

Quantum Physics · Submitted 27 Apr 1999

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

The authors' main claim It is shown that the Darboux transformation operator is unbounded but closed and can not realize an isometric mapping between Hilbert spaces.

how it is stated · asserted 1.00 read the record →

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arXiv IDquant-ph/9904090 (version 1)
Pith IDA32J53OG, Pith's permanent record of this paper and its review
CitationBoris F. Samsonov. "Coherent States for Transparent Potentials." arXiv:quant-ph/9904090 (1999). https://pith.science/paper/A32J53OG
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,502 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.80 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.15 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Darboux transformation operators that produce multisoliton potentials are analyzed as operators acting in a Hilbert space. Isometric correspondence between Hilbert spaces of states of a free particle and a particle moving in a soliton potential is established. It is shown that the Darboux transformation operator is unbounded but closed and can not realize an isometric mapping between Hilbert spaces. A quasispectral representation of such an operator in terms of continuum bases is obtained. Different types of coherent states of a multisoliton potential are introduced. Measures that realize the resolution of the identity operator in terms of the projectors on the coherent states vectors are calculated. It is shown that when these states are related with free particle coherent states by a bounded symmetry operator the measure is defined by ordinary functions and in the case of a semibounded symmetry operator the measure is defined by a generalized function.

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 Darboux transformation operators that produce multisoliton potentials are analyzed as operators acting in a Hilbert space. contribution 0.61 0.58 0.05 asserted 0.94
s1 Isometric correspondence between Hilbert spaces of states of a free particle and a particle moving in a soliton potential is established. result 0.67 0.79 0.12 asserted 1.00
s2 It is shown that the Darboux transformation operator is unbounded but closed and can not realize an isometric mapping between Hilbert spaces. result 0.97 0.82 0.42 asserted 1.00
s3 A quasispectral representation of such an operator in terms of continuum bases is obtained. result 0.42 0.89 0.06 asserted 1.00
s4 Different types of coherent states of a multisoliton potential are introduced. contribution 0.99 0.89 0.08 asserted 0.99
s5 Measures that realize the resolution of the identity operator in terms of the projectors on the coherent states vectors are calculated. result 0.70 0.91 0.11 asserted 1.00
s6 It is shown that when these states are related with free particle coherent states by a bounded symmetry operator the measure is defined by ordinary functions and in the case of a semibounded symmetry operator the measure is defined by a generalized function. result 0.99 0.89 0.28 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v1
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

Darboux transformation operators that produce multisoliton potentials are analyzed as operators acting in a Hilbert space. Isometric correspondence between Hilbert spaces of states of a free particle and a particle moving in a soliton potential is established. It is shown that the Darboux transformation operator is unbounded but closed and can not realize an isometric mapping between Hilbert spaces. A quasispectral representation of such an operator in terms of continuum bases is obtained. Different types of coherent states of a multisoliton potential are introduced. Measures that realize the resolution of the identity operator in terms of the projectors on the coherent states vectors are calculated. It is shown that when these states are related with free particle coherent states by a bounded symmetry operator the measure is defined by ordinary functions and in the case of a semibounded symmetry operator the measure is defined by a generalized function.

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