势函数V（x）= Ax^a + Bx^b能量本征值的多点拟有理逼近
Multi-point quasi-rational approximants for the energy eigenvalues of potentials of the form V(x)= Ax^a + Bx^b
摘要：
利用多点拟有理逼近技术，得到了势为$V(x)= Ax^a + Bx^b$的一维薛定谔方程本征值的解析逼近.该方法基于$λ=A^{-\frac{b+2}{a+2}}B$中特征值的幂级数和渐近展开以及中间点处的展开。这些展开式是通过一个微分方程组得到的。找到的近似值对于任何$λ$值都是有效和准确的。作为例子，该方法被应用于四次和六次非谐振子。
英文摘要：
Analytic approximants for the eigenvalues of the one-dimensional Schrödinger equation with potentials of the form $V(x)= Ax^a + Bx^b$ are found using a multi-point quasi-rational approximation technique. This technique is based on the use of the power series and asymptotic expansion of the eigenvalues in $λ=A^{-\frac{b+2}{a+2}}B$, as well as the expansion at intermediate points. These expansions are found through a system of differential equations. The approximants found are valid and accurate for any value of $λ$. As examples, the technique is applied to the quartic and sextic anharmonic oscillators.
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