Perturbation of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier

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 V0{V}_{0} in height and 2c2c in width, where V0{V}_{0} is assumed to be greater than the energy E of the particle under consideration.

Keywords

• perturbations
• hyers-ulam stability
• schrödinger equation
• time-independent schrödinger equation
• potential barrier
• 34d10
• 34a40
• 34a45
• 39b82
• 41a30