Application of Laskin Fractional Quantum mechanics with a changed fractional differential operator to one-dimensional potentials
DOI:
https://doi.org/10.31349/RevMexFis.71.020703Keywords:
Fractional quantum mechanics; 1D problems; Riemann-Liouville-Caputo formulation; conformable formulationAbstract
We studied the quantum mechanics problem of certain one-dimensional potential functions using Laskin fractional quantum mechanics. We used different representations to describe the kinetic energy operator, including the conformable and Riemann-Liouville-Caputo fractional differential operators. We then compared each approach's energy states and wave function outcomes for single and double rectangular and harmonic potentials. As the fractional index increased, there was a noticeable difference between the excited level energy values resulting from each method. Additionally, we find a noticeable change in the probability density when the system exhibits degenerate states. Our results provide a straightforward and standardized approach for solving the one-dimensional fractional Schrödinger equation numerically.
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Copyright (c) 2025 L. Y. Medina, J. D. Correa, M. E. Mora-Ramos, J. F. Pérez-Torres
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