Convergence of scaled delta expansion: Anharmonic oscillator

Riccardo Guida, Kenichi Konishi, Hiroshi Suzuki

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Abstract

We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency Ω is chosen to scale with the order as Ω = CNγ; 1/3 < γ < 1/2, C > 0 as N → ∞. It converges also for γ = 1/3, if C ≥ αcg1/3, αc ≃ 0.570875, where g is the coupling constant in front of the operator q4/4. The extreme case with γ = 1/3, C = γcg1/3 corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones.

Original languageEnglish
Pages (from-to)152-184
Number of pages33
JournalAnnals of Physics
Volume241
Issue number1
DOIs
Publication statusPublished - Jul 1995

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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