广义Rayleigh-Schroedinger微扰理论作为所谓准精确可解模型线性化方法
Generalized Rayleigh-Schroedinger perturbation theory as a method of linearization of the so called quasi-exactly solvable models
AI总结：
针对D维六次谐振子这一典型准精确可解模型，提出一种与N无关的线性方法，通过1/√D幂级数展开，在前两阶实现所有QES态的精确可解性，并给出整数运算的显式矩阵公式。
摘要：
考虑D维六次谐振子作为典型的准精确可解（QES）模型。通常，其QES N重束缚态必须使用耦合的Magyari非线性代数方程计算。我们提出并描述了一种替代的线性方法，该方法与N无关，并使用1/√D的幂级数展开。主要优点：在前两阶（简并完全消除，未微扰谱等距）同时实现精确可解性（对所有QES态）。附加优点：所有微扰修正由整数运算中的显式矩阵公式给出（没有舍入误差）。
英文摘要：
Sextic oscillator in D dimensions is considered as a typical quasi-exactly solvable (QES) model. Usually, its QES N-plets of bound states have to be computed using the coupled Magyari's nonlinear algebraic equations. We propose and describe an alternative linear method which is N-independent and works with power series in 1/\sqrt(D). Main merit: simultaneous exact solvability (for all the QES states) in the first two leading orders (the degeneracy is completely removed, the unperturbed spectrum is equidistant). An additional merit: All the perturbation corrections are given by explicit matrix formulae in integer arithmetics (there are no rounding errors).
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