标题： 四个五参数独立合流Heun势和五个四参数独立合流Heun势用于定态Klein-Gordon方程 显示英文标题

标题： Four five-parametric and five four-parametric independent confluent Heun potentials for the stationary Klein-Gordon equation

摘要： 我们总共提出了十五种势，这些势的定态克莱因-戈登方程可以用合流赫恩函数来求解。 由于合流赫恩方程在其正则奇点交换下的对称性，只有九种势是独立的。 这九种独立势中有四种是五参数的。 其中一种势包含一个四参数的普通超几何子势，另一种包含一个四参数的合流超几何子势，还有一种势同时包含两种类型的四参数超几何子势。 第四种五参数势有一个三参数的合流超几何子势，但该子势仅在条件可积的情况下才能求解。 其余五个独立的赫恩势是四参数的，并且其解只能用不可约的合流赫恩函数来表示。 显示英文摘要

摘要： We present in total fifteen potentials for which the stationary Klein-Gordon equation is solvable in terms of the confluent Heun functions. Because of the symmetry of the confluent Heun equation with respect to the transposition of its regular singularities, only nine of the potentials are independent. Four of these independent potentials are five-parametric. One of them possesses a four-parametric ordinary hypergeometric sub-potential, another one possesses a four-parametric confluent hypergeometric sub-potential, and one potential possesses four-parametric sub-potentials of both hypergeometric types. The fourth five-parametric potential has a three-parametric confluent hypergeometric sub-potential, which is, however, only conditionally integrable. The remaining five independent Heun potentials are four-parametric and have solutions only in terms of irreducible confluent Heun functions.