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

Author

Listed:
  • Ginkyu Choi

    (Department of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, Sejong 30016, Korea
    These authors contributed equally to this work.)

  • Soon-Mo Jung

    (Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Ginkyu Choi & Soon-Mo Jung, 2020. "The Approximation Property of a One-Dimensional, Time Independent Schrödinger Equation with a Hyperbolic Potential Well," Mathematics, MDPI, vol. 8(8), pages 1-8, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1351-:d:398030
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    References listed on IDEAS

    as
    1. Ginkyu Choi & Soon-Mo Jung & Jaiok Roh, 2019. "Some Properties of Approximate Solutions of Linear Differential Equations," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    2. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, June.
    Full references (including those not matched with items on IDEAS)

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