论文标题
Schrödinger方程，用于两个准确解决的电位
Schrödinger equation for two quasi-exactly solvable potentials
论文作者
论文摘要
我们将HEUN通用方程式的解决方案应用于固定的Schrödinger方程，并具有两个准确解决的椭圆电位，这些椭圆势取决于实际参数$ \ ell $。如果$ \ ell $是整数，则我们从HEUN方程的Power系列扩展中获得有限序列解决方案，除非$ \ ell = -1，-2，-2，-3，-4 $。如果$ \ ell \ neq-5/2 $是奇数整数的一半，则在超几何功能方面获得有限序列。准脱机可溶性由有限的串联解决方案表示。但是，对于任何$ \ ell $的值，我们找到无限序列的特征函数，这些特征函数对自变量的所有值都收敛且有限。
We apply solutions of Heun's general equation to the stationary Schrödinger equation with two quasi-exactly solvable elliptic potentials which depend on a real parameter $\ell$. We get finite-series solutions from power series expansions for Heun's equation if $\ell$ is an integer, except if $\ell=-1,-2,-3,-4$. If $\ell\neq-5/2$ is half an odd integer, we obtain finite series in terms of hypergeometric functions. The quasi-exact solvability is expressed by the finite series solutions. However, for any value of $\ell$, we find infinite-series eigenfunctions which are convergent and bounded for all values of the independent variable.
