The Approximation Property of a One-Dimensional, Time Independent Schrödinger Equation with a Hyperbolic Potential Well

Ginkyu Choi and Soon-Mo Jung
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Ginkyu Choi: Department of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, Sejong 30016, Korea
Soon-Mo Jung: Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea

Mathematics, 2020, vol. 8, issue 8, 1-8

Abstract: 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.

Keywords: generalized Hyers–Ulam stability; Hyers–Ulam stability; Schrödinger equation; time independent Schrödinger equation; hyperbolic potential well (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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