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A New Kind of Deformed Hermite Polynomials and Its Applications

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Si Cong Jing, Wei Min Yang

Mathematical Physics · Submitted 3 Dec 2002

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

The authors' main claim As its applications, we calculate explicit forms of parabose squeezed number states, derive a particularly simple subset of minimum uncertainty states for parabose amplitude-squared squeezing, and discuss their basic squeezing behaviours.

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arXiv IDmath-ph/0212011 (version 1)
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CitationSi Cong Jing, Wei Min Yang. "A New Kind of Deformed Hermite Polynomials and Its Applications." arXiv:math-ph/0212011 (2002). https://pith.science/paper/CKDTBGKI
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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, 2,991 input tokens.

What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating function, orthonormality, differential and integral representaions, and recursion relations are also discussed in this paper. As its applications, we calculate explicit forms of parabose squeezed number states, derive a particularly simple subset of minimum uncertainty states for parabose amplitude-squared squeezing, and discuss their basic squeezing behaviours.

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 A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. background 0.99 0.09 0.04 asserted 1.00
s1 Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating function, orthonormality, differential and integral representaions, and recursion relations are also discussed in this paper. contribution 1.00 0.92 0.19 asserted 1.00
s2 As its applications, we calculate explicit forms of parabose squeezed number states, derive a particularly simple subset of minimum uncertainty states for parabose amplitude-squared squeezing, and discuss their basic squeezing behaviours. result 0.74 0.96 0.40 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 1.00.

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  • references and citing sentences
  • relations to other papers
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  • T body sentences
  • C citations
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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

A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating function, orthonormality, differential and integral representaions, and recursion relations are also discussed in this paper. As its applications, we calculate explicit forms of parabose squeezed number states, derive a particularly simple subset of minimum uncertainty states for parabose amplitude-squared squeezing, and discuss their basic squeezing behaviours.

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