Analytical Solution of the Time-Fractional Schrödinger Equation via Decomposition Methods and Series Expansions
DOI:
https://doi.org/10.26577/RCPh2025952Keywords:
analytical fractional modeling, fractional Schrödinger equation, nonlocal quantum memory, Adomian decomposition method, analytical fractional modeling nechanicsAbstract
Understanding quantum systems with intrinsic memory and spatial nonlocality requires mathematical models beyond the limits of classical calculus. In this work, the one-dimensional time-fractional Schrödinger equation is examined through a hybrid analytical framework combining the Aboodh transform with the Adomian Decomposition Method. This formulation enables the reconstruction of the wave function as a rapidly convergent analytical series. The fractional order (α) appears as a physically significant quantity that influences both the energy spectrum and the temporal evolution of quantum states. The theoretical outcomes are compared with optical band-gap variations observed experimentally in ZnO and Al-doped ZnO nanostructures, demonstrating that the fractional model provides a coherent correspondence between theory and measurable quantum behavior. Furthermore, the proposed approach exhibits superior stability and reduced computational effort compared with traditional Laplace and Fourier schemes, making it adaptable to a wide range of fractional quantum models..
References
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