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Uniform Asymptotic Solutions of a System of two Schr\"odinger Equations with Potential-Curve-Crossing Point

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Irina Jakushina

High Energy Physics - Theory · Submitted 26 Apr 1994

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

The authors' main claim A formal uniform asymptotic solution of the system of differential equations $ h^{2}\frac{d^{2}U_{1}}{dz^{2}}+\Phi_{1} U_{1}=\alpha U_{2} $ , $ h^{2}\frac{d^{2}U_{2}}{dz^{2}}+\Phi_{2} U_{2}=\alpha U_{1}$ , for $ z\in D$ and for h real, large is obtained, when D contains curve-crossing point.

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arXiv IDhep-th/9404161 (version 1)
Pith ID6EUDN4AA, Pith's permanent record of this paper and its review
CitationIrina Jakushina. "Uniform Asymptotic Solutions of a System of two Schr\"odinger Equations with Potential-Curve-Crossing Point." arXiv:hep-th/9404161 (1994). https://pith.science/paper/6EUDN4AA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,136 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

A formal uniform asymptotic solution of the system of differential equations $ h^{2}\frac{d^{2}U_{1}}{dz^{2}}+\Phi_{1} U_{1}=\alpha U_{2} $ , $ h^{2}\frac{d^{2}U_{2}}{dz^{2}}+\Phi_{2} U_{2}=\alpha U_{1}$ , for $ z\in D$ and for h real, large is obtained, when D contains curve-crossing point. Asymptotic approximations for the solutions are constructed in terms of parabolic cylinder functions. Analytical properties of the expansion's coefficients are investigated.The case of potantial barier is also considered.

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 formal uniform asymptotic solution of the system of differential equations $ h^{2}\frac{d^{2}U_{1}}{dz^{2}}+\Phi_{1} U_{1}=\alpha U_{2} $ , $ h^{2}\frac{d^{2}U_{2}}{dz^{2}}+\Phi_{2} U_{2}=\alpha U_{1}$ , for $ z\in D$ and for h real, large is obtained, when D contains curve-crossing point. contribution 0.70 0.93 0.80 asserted 1.00
s1 Asymptotic approximations for the solutions are constructed in terms of parabolic cylinder functions. method 0.94 0.92 0.17 asserted 1.00
s2 Analytical properties of the expansion's coefficients are investigated.The case of potantial barier is also considered. contribution 0.96 0.91 0.09 asserted 0.98

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

A formal uniform asymptotic solution of the system of differential equations $ h^{2}\frac{d^{2}U_{1}}{dz^{2}}+\Phi_{1} U_{1}=\alpha U_{2} $ , $ h^{2}\frac{d^{2}U_{2}}{dz^{2}}+\Phi_{2} U_{2}=\alpha U_{1}$ , for $ z\in D$ and for h real, large is obtained, when D contains curve-crossing point. Asymptotic approximations for the solutions are constructed in terms of parabolic cylinder functions. Analytical properties of the expansion's coefficients are investigated.The case of potantial barier is also considered.

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