Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials

Document Type : Research Paper

Authors

1 Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, PO Box 532, Beni Mellal, 23000, Morocco.

2 Department of Mathematics and Computer Science, Faculty of Sciences, PO Box 2121, Tetouan, Morocco.

Abstract

This paper employs Colombeau algebra as a mathematical framework to establish both the existence and uniqueness of solutions for the fractional Schrödinger equation when subjected to singular potentials. A noteworthy contribution lies in the introduction of the concept of a generalized conformable semigroup, marking the first instance of its application. This innovative approach plays a pivotal role in demonstrating the sought-after results within the context of the fractional Schrödinger equation. The utilization of Colombeau algebra, coupled with the introduction of the generalized conformable semigroup, represents a novel and effective strategy for addressing challenges posed by singular potentials in the study of this particular type of Schrödinger equation.

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Main Subjects

References

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Computational Methods for Differential Equations
Volume 13, Issue 2
March 2025
Pages 373-383

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History

  • Receive Date: 18 April 2023
  • Revise Date: 04 May 2024
  • Accept Date: 25 June 2024

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