论文标题
自适应扰动法的准确研究
Accurate Study from Adaptive Perturbation Method
论文作者
论文摘要
自适应扰动方法通过对角元素和Fock状态的非对角线元素分解了哈密顿量。 Fock状态的对角线元素是可以解决的，但可以包含有关耦合常数的信息。我们研究具有交互潜力的谐波振荡器，$λ_1x^4/6+λ_2X^6/120 $，其中$λ_1$和$λ_2$是耦合常数，而$ x $是位置操作员。在这项研究中，每个扰动项都有一个精确的解决方案。我们证明了对频谱和$ \ langle x^2 \ rangle $的准确研究，直到下一个前阶校正。特别是，我们研究了来自倒数质量项的希格斯场类似问题，以证明粒子物理的非平凡应用。
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants. We study the harmonic oscillator with the interacting potential, $λ_1x^4/6+λ_2x^6/120$, where $λ_1$ and $λ_2$ are coupling constants, and $x$ is the position operator. In this study, each perturbed term has an exact solution. We demonstrate the accurate study of the spectrum and $\langle x^2\rangle$ up to the next leading-order correction. In particular, we study a similar problem of Higgs field from the inverted mass term to demonstrate the possible non-trivial application of particle physics.
