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<p>This paper investigates the initial boundary value problem for the quantum mechanics fundamental equation with a fractional Riemann–Liouville derivative in time. A finite-difference modeling approach is employed to approximate the solution, and a corresponding finite-difference scheme is constructed. The well-posedness and stability of the numerical method are analyzed. Additionally, numerical experiments are conducted to illustrate the accuracy and efficiency of the proposed scheme, demonstrating its applicability to problems involving fractional-order quantum dynamics. The results provide insights into the behavior of fractional wave mechanics equations and contribute to the development of reliable computational methods for fractional differential equations.</p>

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Numerical Scheme for the Wave Mechanics Equation with Riemann--Liouville Time Derivative

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Georgy Neverov,
  • Natalia Ivanova

摘要

This paper investigates the initial boundary value problem for the quantum mechanics fundamental equation with a fractional Riemann–Liouville derivative in time. A finite-difference modeling approach is employed to approximate the solution, and a corresponding finite-difference scheme is constructed. The well-posedness and stability of the numerical method are analyzed. Additionally, numerical experiments are conducted to illustrate the accuracy and efficiency of the proposed scheme, demonstrating its applicability to problems involving fractional-order quantum dynamics. The results provide insights into the behavior of fractional wave mechanics equations and contribute to the development of reliable computational methods for fractional differential equations.