具有反平方根奇异性的短程指数势薛定谔方程的精确解
Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity
摘要：
我们引入了一个精确可积的奇异势，一维定常薛定谔方程的解可以通过高斯超几何函数的不可约线性组合来表示。该势属于广义Heun族，是一个短程势，在原点附近表现为平方根的倒数，在无穷远处指数消失。我们导出了能量的精确谱方程，并讨论了势支持的束缚态。
英文摘要：
We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.
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