Abstract In Applied Mathematics Letters 74 (2017), 147–153, the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation was investigated when the relevant system has a potential well of finite depth. As a continuous work, we prove in this paper a type of Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier of V 0 {V}_{0} in height and 2 c 2c in width, where V 0 {V}_{0} is assumed to be greater than the energy E of the particle under consideration.

中文翻译：

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具有矩形势垒的一维时间无关薛定谔方程的扰动

摘要 在 Applied Mathematics Letters 74 (2017), 147–153 中，研究了当相关系统具有有限深度势阱时一维时间无关薛定谔方程的 Hyers-Ulam 稳定性。作为一项连续的工作，我们在本文中证明了具有高度为 V 0 {V}_{0} 和宽度为 2 c 2c 的矩形势垒的一维时间无关薛定谔方程的一种 Hyers-Ulam 稳定性，其中假设 V 0 {V}_{0} 大于所考虑粒子的能量 E。