标题： 标度 delta 展开的收敛性：非简谐振子 显示英文标题

标题： Convergence of Scaled Delta Expansion: Anharmonic Oscillator

摘要： 我们证明，如果采用与展开阶数相关的依序依赖性试验频率 $\Omega$ 并选择其按 \($\Omega=CN^\gamma$;$1/3<\gamma<1/2$,$C>0$\) 作为 $N\rightarrow\infty$ 的形式变化，则量子力学非简谐振子的能量本征值的线性δ展开收敛到精确答案。 它也收敛于$\gamma=1/3$，如果$C\geq\alpha_c g^{1/3}$，$\alpha_c\simeq 0.570875$，其中$g$是算符$q^4/4$前面的耦合常数。 极端情况$\gamma=1/3$，$C=\alpha_cg^{1/3}$对应于 Seznec 和 Zinn-Justin 之前讨论过的选择，最近也由 Duncan 和 Jones 讨论过。 显示英文摘要

摘要： 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 $\Omega=CN^\gamma$; $1/3<\gamma<1/2$, $C>0$ as $N\rightarrow\infty$. It converges also for $\gamma=1/3$, if $C\geq\alpha_c g^{1/3}$, $\alpha_c\simeq 0.570875$, where $g$ is the coupling constant in front of the operator $q^4/4$. The extreme case with $\gamma=1/3$, $C=\alpha_cg^{1/3}$ corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones.