Application of Laskin fractional quantum mechanics with a changed fractional differential operator to one-dimensional potentials
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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 energy values resulting from each method. When the system exhibits degeneracy, we find noticeable changes in the probability densities. Our results provide a straightforward and standardized approach for solving the one-dimensional fractional Schrödinger equation numerically. © (2025), (Sociedad Mexicana de Fisica). All rights reserved.
Palabras clave
1D problems, Conformable formulation, Fractional quantum mechanics, Riemann-Liouville-Caputo formulation