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Perturbation Method beyond the Variational Gaussian Approximation: The Liouville-Neumann Approach

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Dongsu Bak, Sang Pyo Kim, Sung Ku Kim, Kwang-Sup Soh, Jae Hyung Yee

High Energy Physics - Theory · Submitted 1 Aug 1998

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

The authors' main claim We have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent systems.

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arXiv IDhep-th/9808001 (version 3)
Pith IDY5U6XA2Y, Pith's permanent record of this paper and its review
CitationDongsu Bak, Jae Hyung Yee, Kwang-Sup Soh, Sang Pyo Kim, Sung Ku Kim. "Perturbation Method beyond the Variational Gaussian Approximation: The Liouville-Neumann Approach." arXiv:hep-th/9808001 (1998). https://pith.science/paper/Y5U6XA2Y
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,965 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent systems. We then apply the method to the time-independent anharmonic oscillator, and show that the results agree with those of other variational perturbation theories. We also show that the system has an interesting algebraic structure at the first order correction level.

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 have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent systems. contribution 0.81 0.96 0.49 asserted 1.00
s1 We then apply the method to the time-independent anharmonic oscillator, and show that the results agree with those of other variational perturbation theories. result 0.83 0.95 0.23 asserted 1.00
s2 We also show that the system has an interesting algebraic structure at the first order correction level. result 0.97 0.94 0.11 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.90.

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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

We have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent systems. We then apply the method to the time-independent anharmonic oscillator, and show that the results agree with those of other variational perturbation theories. We also show that the system has an interesting algebraic structure at the first order correction level.

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