Convergence of scaled delta expansion: Anharmonic oscillator

Riccardo Guida, Kenichi Konishi, Hiroshi Suzuki

Research output: Contribution to journalArticlepeer-review

112 Citations (Scopus)


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
Issue number1
Publication statusPublished - Jul 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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