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L2 series solutions of the Dirac equation for power-law potentials at rest mass energy

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A. D. Alhaidari

Mathematical Physics · Submitted 6 Jun 2004

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

The authors' main claim We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions.

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arXiv IDmath-ph/0406012 (version 1)
Pith IDJEXUC5V5, Pith's permanent record of this paper and its review
CitationA. D. Alhaidari. "L2 series solutions of the Dirac equation for power-law potentials at rest mass energy." arXiv:math-ph/0406012 (2004). https://pith.science/paper/JEXUC5V5
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,241 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the Dirac operator is tridiagonal. The "wave equation" results in a three-term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials. These are modified versions of the Meixner-Pollaczek polynomials and of the continuous dual Hahn polynomials. The choice depends on the values of the angular momentum and the power of the potential.

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 We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. contribution 0.81 0.96 0.79 asserted 1.00
s1 These are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the Dirac operator is tridiagonal. method 0.90 0.91 0.09 asserted 1.00
s2 The "wave equation" results in a three-term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials. method 0.88 0.85 0.15 asserted 1.00
s3 These are modified versions of the Meixner-Pollaczek polynomials and of the continuous dual Hahn polynomials. result 0.72 0.70 0.09 asserted 1.00
s4 The choice depends on the values of the angular momentum and the power of the potential. method 0.45 0.68 0.05 asserted 0.99

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

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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

We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the Dirac operator is tridiagonal. The "wave equation" results in a three-term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials. These are modified versions of the Meixner-Pollaczek polynomials and of the continuous dual Hahn polynomials. The choice depends on the values of the angular momentum and the power of the potential.

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