A type of Hyers–Ulam stability of the one-dimensional, time independent Schrödinger equation was recently investigated; the relevant system had a parabolic potential wall. As a continuation, we proved a type of Hyers–Ulam stability of the time independent Schrödinger equation under the action of a specific hyperbolic potential well. One of the advantages of this paper is that it proves a type of Hyers–Ulam stability of the Schrödinger equation under the condition that the potential function has singularities.

中文翻译：

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具有双曲势阱的一维，时间独立的Schrödinger方程的逼近性质

一维，时间无关的薛定ding方程的一种Hyers-Ulam稳定性最近得到了研究；相关系统具有抛物线形势垒。作为继续，我们证明了在特定双曲线势阱的作用下，与时间无关的薛定ding方程的一种Hyers-Ulam稳定性。本文的优点之一是证明了势函数具有奇异性的条件下Schrödinger方程的Hyers-Ulam稳定性。