Convergence of Scaled Delta Expansion: Anharmonic Oscillator

✍ Scribed by R. Guida; K. Konishi; H. Suzuki

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 991 KB
• Volume: 241
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1995.1059

✦ Synopsis

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 (\Omega) is chosen to scale with the order as (\Omega=C N^{\gamma} ; 1 / 3<\gamma<1 / 2, C>0) as (N \rightarrow \infty). It converges also for (\gamma=1 / 3), if (C \geqslant \alpha_{c} g^{1 / 3}, \alpha_{r} \simeq 0.570875), where (g) is the coupling constant in front of the operator (q^{4} / 4). The extreme case with (\gamma=1 / 3, C=\alpha_{c} g^{1 / 3}) corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones. C 1995 Academic Press. Inc.